Spontaneous Lorentz violation, Nambu-Goldstone modes, and gravity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 6, 2005, Pages 1-17

  Bluhm, Robert ^a   Kostelecký, V Alan ^b  

^a Health Services and Department of Biology   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION; ARTICLE; BOSON; DYNAMICS; GRAVITY; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; VACUUM;

EID: 18544373989     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.065008     Document Type: Article

References (159)

1. For recent reviews of various experimental and theoretical approaches to Lorentz and CPT violation see, for example, CPT and Lorentz Symmetry III edited by V. A. Kostelecký (World Scientific, Singapore, 2005) and earlier volumes in this series: CPT and Lorentz Symmetry II (World Scientific, Singapore, 2002); CPT and Lorentz Symmetry (World Scientific, Singapore, 1999).
2. For recent reviews of various experimental and theoretical approaches to Lorentz and CPT violation see, for example, CPT and Lorentz Symmetry III edited by V. A. Kostelecký (World Scientific, Singapore, 2005) and earlier volumes in this series: CPT and Lorentz Symmetry II (World Scientific, Singapore, 2002); CPT and Lorentz Symmetry (World Scientific, Singapore, 1999).
3. For recent reviews of various experimental and theoretical approaches to Lorentz and CPT violation see, for example, CPT and Lorentz Symmetry III edited by V. A. Kostelecký (World Scientific, Singapore, 2005) and earlier volumes in this series: CPT and Lorentz Symmetry II (World Scientific, Singapore, 2002); CPT and Lorentz Symmetry (World Scientific, Singapore, 1999).
4. V. A. Kostelecký and S. Samuel, Phys. Rev. D 39, 683 (1989); V. A. Kostelecký and R. Potting, Nucl. Phys. B359, 545 (1991).
5. V. A. Kostelecký and S. Samuel, Phys. Rev. D 39, 683 (1989); V. A. Kostelecký and R. Potting, Nucl. Phys. B359, 545 (1991).
6. Y. Nambu, Phys. Rev. Lett. 4, 380 (1960); J. Goldstone, Nuovo Cimento 19, 154 (1961); J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962).
7. Y. Nambu, Phys. Rev. Lett. 4, 380 (1960); J. Goldstone, Nuovo Cimento 19, 154 (1961); J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962).
8. Y. Nambu, Phys. Rev. Lett. 4, 380 (1960); J. Goldstone, Nuovo Cimento 19, 154 (1961); J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962).
9. F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964).
10. F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964).
11. F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964).
12. V. A. Kostelecký, Phys. Rev. D 69, 105 009 (2004).
13. V. A. Kostelecký and R. Potting, Phys. Rev. D 51, 3923 (1995).
14. D. Colladay and V. A. Kostelecký, Phys. Rev. D 55, 6760 (1997); Phys. Rev. D 58, 116002 (1998).
15. D. Colladay and V. A. Kostelecký, Phys. Rev. D 55, 6760 (1997); Phys. Rev. D 58, 116002 (1998).
16. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
17. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
18. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
19. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
20. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
21. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
22. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
23. J. Lipa et al., Phys. Rev. Lett. 90, 060 403 (2003); H. Müller et al., Phys. Rev. Lett. 91, 020 401 (2003); P. Wolf et al., Gen. Relativ. Gravit. 36, 2351 (2004); Phys. Rev. D 70, 051902 (2004); S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990); M. P. Haugan and T. F. Kauffmann, Phys. Rev. D 52, 3168 (1995); V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 87, 251 304 (2001); Phys. Rev. D 66, 056005 (2002).
24. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
25. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
26. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
27. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
28. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
29. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
30. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
31. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
32. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
33. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
34. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
35. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
36. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
37. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
38. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
39. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
40. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
41. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
42. For theoretical discussions of Lorentz violation in electrodynamics see, for example, R. Jackiw and V. A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999); M. Pérez-Victoria, J. High Energy Phys. 04 (2001) 032; V. A. Kostelecký, C. D. Lane, and A. G. M. Pickering, Phys. Rev. D 65, 056006 (2002); C. Adam and F. R. Klinkhamer, Nucl. Phys. B657, 214 (2003); H. Müller et al., Phys. Rev. D 67, 056006 (2003); T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003); V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031 801 (2003); R. Lehnert, Phys. Rev. D 68, 085003 (2003); G. M. Shore, Contemp. Phys. 44, 503 (2003); B. Altschul, Phys. Rev. D 69, 125009 (2004); Phys. Rev. D 70, 101701 (2004); hep-th/0402036; T. Jacobson, S. Liberati, D. Mattingly, and F. Stecker, Phys. Rev. Lett. 93, 021101 (2004); R. Lehnert and R. Potting, Phys. Rev. Lett. 93, 110 402 (2004); Phys. Rev. D 70, 125010 (2004); Phys. Rev. D 70, 129906(E) (2004); F. R. Klinkhamer and C. Rupp, Phys. Rev. D 70, 045020 (2004); Q. Bailey and V. A. Kostelecký, Phys. Rev. D 70, 076006 (2004); C. Lämmerzahl, A. Macias, and H. Müller, Phys. Rev. D 71, 025007 (2005); C. Lämmerzahl and F. W. Hehl, Phys. Rev. D 70, 105022 (2004); H. Belich, T. Costa-Soares, M. M. Ferreira, and J. A. Helayel-Neto, hep-th/0411151.
43. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
44. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
45. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
46. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
47. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
48. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
49. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
50. H. Dehmelt et al., Phys. Rev. Lett. 83, 4694 (1999); R. Mittleman et al., Phys. Rev. Lett. 83, 2116 (1999); G. Gabrielse et al., Phys. Rev. Lett. 82, 3198 (1999); R. Bluhm et al., Phys. Rev. Lett. 82, 2254 (1999); Phys. Rev. Lett. 79, 1432 (1997); Phys. Rev. D 57, 3932 (1998); D. Colladay and V. A. Kostelecký, Phys. Lett. B 511, 209 (2001); B. Altschul, Phys. Rev. D 70, 056005 (2004); G. Shore, hep-th/0409125.
51. B. Heckel, in CPT and Lorentz Symmetry III (Ref. [1]); L.-S. Hou, W.-T. Ni, and Y.-C. M. Li, Phys. Rev. Lett. 90, 201 101 (2003); R. Bluhm and V. A. Kostelecký, Phys. Rev. Lett. 84, 1381 (2000).
52. B. Heckel, in CPT and Lorentz Symmetry III (Ref. [1]); L.-S. Hou, W.-T. Ni, and Y.-C. M. Li, Phys. Rev. Lett. 90, 201 101 (2003); R. Bluhm and V. A. Kostelecký, Phys. Rev. Lett. 84, 1381 (2000).
53. B. Heckel, in CPT and Lorentz Symmetry III (Ref. [1]); L.-S. Hou, W.-T. Ni, and Y.-C. M. Li, Phys. Rev. Lett. 90, 201 101 (2003); R. Bluhm and V. A. Kostelecký, Phys. Rev. Lett. 84, 1381 (2000).
54. H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lämmerzahl, Phys. Rev. D 68, 116006 (2003); Phys. Rev. D 70, 076004 (2004).
55. H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lämmerzahl, Phys. Rev. D 68, 116006 (2003); Phys. Rev. D 70, 076004 (2004).
56. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
57. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
58. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
59. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
60. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
61. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
62. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
63. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
64. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
65. L. R. Hunter et al., in CPT and Lorentz Symmetry (Ref. [1]); D. Bear et al., Phys. Rev. Lett. 85, 5038 (2000); D. F. Phillips et al., Phys. Rev. D 63, 111101 (2001); M. A. Humphrey et al., Phys. Rev. A 68, 063807 (2003); Phys. Rev. A 62, 063405 (2000); F. Canè et al., Phys. Rev. Lett. 93, 230 801 (2004); V. A. Kostelecký and C. D. Lane, Phys. Rev. D 60, 116010 (1999); J. Math. Phys. (N.Y.) 40, 6245 (1999); R. Bluhm et al., Phys. Rev. Lett. 88, 090 801 (2002); Phys. Rev. D 68, 125008 (2003).
66. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
67. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
68. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
69. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
70. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
71. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
72. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
73. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
74. KTeV Collaboration, H. Nguyen, in CPT and Lorentz Symmetry II (Ref. [1]); OPAL Collaboration, R. Ackerstaff et al., Z. Phys. C 76, 401 (1997); DELPHI Collaboration, M. Feindt et al., DELPHI Report No. 97-98 CONF 80, 1997; BELLE Collaboration, K. Abe et al., Phys. Rev. Lett. 86, 3228 (2001); BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 92, 142 002 (2004); FOCUS Collaboration, J. M. Link et al., Phys. Lett. B 556, 7 (2003); V. A. Kostelecký, Phys. Rev. Lett. 80, 1818 (1998); Phys. Rev. D 61, 016002 (2000); Phys. Rev. D 64, 076001 (2001).
75. V. W. Hughes et al., Phys. Rev. Lett. 87, 111 804 (2001); R. Bluhm et al., Phys. Rev. Lett. 84, 1098 (2000).
76. V. W. Hughes et al., Phys. Rev. Lett. 87, 111 804 (2001); R. Bluhm et al., Phys. Rev. Lett. 84, 1098 (2000).
77. Recent experimental studies of Lorentz and CPT violation with neutrinos are summarized in papers by SK Collaboration, M. D. Messier; LSND Collaboration, T. Katori and R. Tayloe; and MINOS Collaboration, B. J. Rebel and S. F. Mufson, all in CPT and Lorentz Symmetry III (Ref. [1]).
78. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
79. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
80. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
81. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
82. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
83. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
84. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
85. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
86. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
87. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
88. For theoretical discussions of Lorentz violation in neutrinos, see Ref. [7] and S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999); V. Barger, S. Pakvasa, T. Weiler, and K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000); J. N. Bahcall, V. Barger, and D. Marfatia, Phys. Lett. B 534, 120 (2002); I. Mocioiu and M. Pospelov, Phys. Lett. B 534, 114 (2002); A. de Gouvêa, Phys. Rev. D 66, 076005 (2002); G. Lambiase, Phys. Lett. B 560, 1 (2003); V. A. Kostelecký and M. Mewes, Phys. Rev. D 69, 016005 (2004); Phys. Rev. D 70, 031902(R) (2004); Phys. Rev. D 70, 076002 (2004); S. Choubey and S. F. King, Phys. Lett. B 586, 353 (2004); A. Datta et al., Phys. Lett. B 597, 356 (2004).
89. D. L. Anderson, M. Sher, and I. Turan, Phys. Rev. D 70, 016001 (2004); E. O. Iltan, Mod. Phys. Lett. A 19, 327 (2004).
90. D. L. Anderson, M. Sher, and I. Turan, Phys. Rev. D 70, 016001 (2004); E. O. Iltan, Mod. Phys. Lett. A 19, 327 (2004).
91. P. A. M. Dirac, Proc. R. Soc. London A. 209, 291 (1951); W. Heisenberg, Rev. Mod. Phys. 29, 269 (1957); P. G. O. Freund, Acta Phys. Austriaca 14, 445 (1961); J. D. Bjorken, Ann. Phys. (N.Y.) 24, 174 (1963).
92. P. A. M. Dirac, Proc. R. Soc. London A. 209, 291 (1951); W. Heisenberg, Rev. Mod. Phys. 29, 269 (1957); P. G. O. Freund, Acta Phys. Austriaca 14, 445 (1961); J. D. Bjorken, Ann. Phys. (N.Y.) 24, 174 (1963).
93. P. A. M. Dirac, Proc. R. Soc. London A. 209, 291 (1951); W. Heisenberg, Rev. Mod. Phys. 29, 269 (1957); P. G. O. Freund, Acta Phys. Austriaca 14, 445 (1961); J. D. Bjorken, Ann. Phys. (N.Y.) 24, 174 (1963).
94. P. A. M. Dirac, Proc. R. Soc. London A. 209, 291 (1951); W. Heisenberg, Rev. Mod. Phys. 29, 269 (1957); P. G. O. Freund, Acta Phys. Austriaca 14, 445 (1961); J. D. Bjorken, Ann. Phys. (N.Y.) 24, 174 (1963).
95. Y. Nambu, Prog. Theor. Phys. Suppl. Extra 190 (1968).
96. H. van Dam and M. Veltman, Nucl. Phys. B22, 397 (1970); V. I. Zakharov, JETP Lett. 12, 312 (1970). A recent discussion of the discontinuity in a non-Minkowski background is F. A. Dilkes, M. J. Duff, J. T. Liu, and H. Sati, Phys. Rev. Lett. 87, 041 301 (2001).
97. H. van Dam and M. Veltman, Nucl. Phys. B22, 397 (1970); V. I. Zakharov, JETP Lett. 12, 312 (1970). A recent discussion of the discontinuity in a non-Minkowski background is F. A. Dilkes, M. J. Duff, J. T. Liu, and H. Sati, Phys. Rev. Lett. 87, 041 301 (2001).
98. H. van Dam and M. Veltman, Nucl. Phys. B22, 397 (1970); V. I. Zakharov, JETP Lett. 12, 312 (1970). A recent discussion of the discontinuity in a non-Minkowski background is F. A. Dilkes, M. J. Duff, J. T. Liu, and H. Sati, Phys. Rev. Lett. 87, 041 301 (2001).
99. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 63, 224 (1989); Phys. Rev. D 40, 1886 (1989).
100. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 63, 224 (1989); Phys. Rev. D 40, 1886 (1989).
101. See, for example, H. B. Nielsen and S. Chadha, Nucl. Phys. B105, 445 (1976); I. Low and A. V. Manohar, Phys. Rev. Lett. 88, 101 602 (2002); Y. Nambu, in CPT and Lorentz Symmetry III (Ref. [1]).
102. See, for example, H. B. Nielsen and S. Chadha, Nucl. Phys. B105, 445 (1976); I. Low and A. V. Manohar, Phys. Rev. Lett. 88, 101 602 (2002); Y. Nambu, in CPT and Lorentz Symmetry III (Ref. [1]).
103. See, for example, H. B. Nielsen and S. Chadha, Nucl. Phys. B105, 445 (1976); I. Low and A. V. Manohar, Phys. Rev. Lett. 88, 101 602 (2002); Y. Nambu, in CPT and Lorentz Symmetry III (Ref. [1]).
104. V. A. Kostelecký and R. Lehnert, Phys. Rev. D 63, 065008 (2001).
105. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B.
106. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
107. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
108. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
109. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
110. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
111. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
112. T. Jacobson and D. Mattingly, Phys. Rev. D 64, 024028 (2001); P. Kraus and E. T. Tomboulis, Phys. Rev. D 66, 045015 (2002); J. W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); C. Eling and T. Jacobson, Phys. Rev. D 69, 064005 (2004); A. Jenkins, Phys. Rev. D 69, 105007 (2004); S. M. Carroll and E. A. Lim, Phys. Rev. D 70, 123525 (2004); E. A. Lim, Phys. Rev. D 71, 063504 (2005); B. M. Gripaios, J. High Energy Phys. 10 (2004) 069; J. L. Chkareuli, C. D. Froggatt, R. N. Mohapatra, and H. B. Nielsen, hep-th/0412225.
113. N. Arkani-Hamed, H.-C. Cheng, M. Luty, and J. Thaler, hep-ph/0407034.
114. R. Utiyama, Phys. Rev. 101, 1597 (1956); T. W. B. Kibble, J. Math. Phys. (N.Y.) 2, 212 (1961).
115. R. Utiyama, Phys. Rev. 101, 1597 (1956); T. W. B. Kibble, J. Math. Phys. (N.Y.) 2, 212 (1961).
116. For reviews of gravitation in Riemann-Cartan spacetimes see, for example, F. W. Hehl et al., Rev. Mod. Phys. 48, 393 (1976); I. L. Shapiro, Phys. Rep. 357, 113 (2002).
117. For reviews of gravitation in Riemann-Cartan spacetimes see, for example, F. W. Hehl et al., Rev. Mod. Phys. 48, 393 (1976); I. L. Shapiro, Phys. Rep. 357, 113 (2002).
118. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 66, 1811 (1991); V. A. Kostelecký and R. Potting, Phys. Lett. B 381, 89 (1996); Phys. Rev. D 63, 046007 (2001); V. A. Kostelecký, M. Perry, and R. Potting, Phys. Rev. Lett. 84, 4541 (2000).
119. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 66, 1811 (1991); V. A. Kostelecký and R. Potting, Phys. Lett. B 381, 89 (1996); Phys. Rev. D 63, 046007 (2001); V. A. Kostelecký, M. Perry, and R. Potting, Phys. Rev. Lett. 84, 4541 (2000).
120. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 66, 1811 (1991); V. A. Kostelecký and R. Potting, Phys. Lett. B 381, 89 (1996); Phys. Rev. D 63, 046007 (2001); V. A. Kostelecký, M. Perry, and R. Potting, Phys. Rev. Lett. 84, 4541 (2000).
121. V. A. Kostelecký and S. Samuel, Phys. Rev. Lett. 66, 1811 (1991); V. A. Kostelecký and R. Potting, Phys. Lett. B 381, 89 (1996); Phys. Rev. D 63, 046007 (2001); V. A. Kostelecký, M. Perry, and R. Potting, Phys. Rev. Lett. 84, 4541 (2000).
122. See, for example, I. Mocioiu, M. Pospelov, and R. Roiban, Phys. Lett. B 489, 390 (2000); S. M. Carroll et al., Phys. Rev. Lett. 87, 141 601 (2001); Z. Guralnik, R. Jackiw, S. Y. Pi, and A. P. Polychronakos, Phys. Lett. B 517, 450 (2001); C. E. Carlson, C. D. Carone, and R. F. Lebed, Phys. Lett. B 518, 201 (2001); A. Anisimov, T. Banks, M. Dine, and M. Graesser, Phys. Rev. D 65, 085032 (2002).
123. See, for example, I. Mocioiu, M. Pospelov, and R. Roiban, Phys. Lett. B 489, 390 (2000); S. M. Carroll et al., Phys. Rev. Lett. 87, 141 601 (2001); Z. Guralnik, R. Jackiw, S. Y. Pi, and A. P. Polychronakos, Phys. Lett. B 517, 450 (2001); C. E. Carlson, C. D. Carone, and R. F. Lebed, Phys. Lett. B 518, 201 (2001); A. Anisimov, T. Banks, M. Dine, and M. Graesser, Phys. Rev. D 65, 085032 (2002).
124. See, for example, I. Mocioiu, M. Pospelov, and R. Roiban, Phys. Lett. B 489, 390 (2000); S. M. Carroll et al., Phys. Rev. Lett. 87, 141 601 (2001); Z. Guralnik, R. Jackiw, S. Y. Pi, and A. P. Polychronakos, Phys. Lett. B 517, 450 (2001); C. E. Carlson, C. D. Carone, and R. F. Lebed, Phys. Lett. B 518, 201 (2001); A. Anisimov, T. Banks, M. Dine, and M. Graesser, Phys. Rev. D 65, 085032 (2002).
125. See, for example, I. Mocioiu, M. Pospelov, and R. Roiban, Phys. Lett. B 489, 390 (2000); S. M. Carroll et al., Phys. Rev. Lett. 87, 141 601 (2001); Z. Guralnik, R. Jackiw, S. Y. Pi, and A. P. Polychronakos, Phys. Lett. B 517, 450 (2001); C. E. Carlson, C. D. Carone, and R. F. Lebed, Phys. Lett. B 518, 201 (2001); A. Anisimov, T. Banks, M. Dine, and M. Graesser, Phys. Rev. D 65, 085032 (2002).
126. See, for example, I. Mocioiu, M. Pospelov, and R. Roiban, Phys. Lett. B 489, 390 (2000); S. M. Carroll et al., Phys. Rev. Lett. 87, 141 601 (2001); Z. Guralnik, R. Jackiw, S. Y. Pi, and A. P. Polychronakos, Phys. Lett. B 517, 450 (2001); C. E. Carlson, C. D. Carone, and R. F. Lebed, Phys. Lett. B 518, 201 (2001); A. Anisimov, T. Banks, M. Dine, and M. Graesser, Phys. Rev. D 65, 085032 (2002).
127. V. A. Kostelecký, R. Lehnert, and M. Perry, Phys. Rev. D 68, 123511 (2003).
128. R. Jackiw and S. Y. Pi, Phys. Rev. D 68, 104012 (2003).
129. N. Arkani-Hamed, H.-C. Cheng, M. Luty, and S. Mukohyama, J. High Energy Phys. 05 (2004) 074.
130. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
131. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
132. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
133. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
134. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
135. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
136. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
137. See, for example, R. Gambini and J. Pullin, in CPT and Lorentz Symmetry II (Ref. [1]); J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia, Phys. Rev. D 66, 124006 (2002); D. Sudarsky, L. Urrutia, and H. Vucetich, Phys. Rev. Lett. 89, 231 301 (2002); Phys. Rev. D 68, 024010 (2003); G. Amelino-Camelia, Mod. Phys. Lett. A 17, 899 (2002); Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); R. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211 601 (2003); N. E. Mavromatos, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 1 (2004).
138. C. D. Froggatt and H. B. Nielsen, hep-ph/0211106.
139. J. D. Bjorken, Phys. Rev. D 67, 043508 (2003).
140. See, for example, C. P. Burgess, J. Cline, E. Filotas, J. Matias, and G. D. Moore, J. High Energy Phys. 03 (2002) 043; A. R. Frey, J. High Energy Phys. 04 (2003) 012; J. Cline and L. Valcárcel, J. High Energy Phys. 03 (2004) 032.
141. See, for example, C. P. Burgess, J. Cline, E. Filotas, J. Matias, and G. D. Moore, J. High Energy Phys. 03 (2002) 043; A. R. Frey, J. High Energy Phys. 04 (2003) 012; J. Cline and L. Valcárcel, J. High Energy Phys. 03 (2004) 032.
142. See, for example, C. P. Burgess, J. Cline, E. Filotas, J. Matias, and G. D. Moore, J. High Energy Phys. 03 (2002) 043; A. R. Frey, J. High Energy Phys. 04 (2003) 012; J. Cline and L. Valcárcel, J. High Energy Phys. 03 (2004) 032.
143. CPT is a discrete symmetry, so no new NG modes accompany its spontaneous breaking. The NG modes for Lorentz violation are, however, expected to be present if CPT is broken because CPT violation is accompanied by Lorentz violation in conventional field theories. See O. W. Greenberg, Phys. Rev. Lett. 89, 231 602 (2002); Phys. Lett. B 567, 179 (2003).
144. CPT is a discrete symmetry, so no new NG modes accompany its spontaneous breaking. The NG modes for Lorentz violation are, however, expected to be present if CPT is broken because CPT violation is accompanied by Lorentz violation in conventional field theories. See O. W. Greenberg, Phys. Rev. Lett. 89, 231 602 (2002); Phys. Lett. B 567, 179 (2003).
145. Under special circumstances more than 10 generators are involved. For example, in a theory based on special relativity with multiple noninteracting particle species, there are distinct particle Lorentz transformations for each field. The particle symmetry group of the theory then contains a direct product of several Lorentz groups, and so there could be multiple sets of NG modes. However, in typical gravitational theories with the metric coupling to all irreducible tensors, the full particle invariance involves only one copy of the particle Lorentz and diffeomorphism groups, so only ten corresponding NG modes can appear.
146. D. M. Eardley, D. L. Lee, A. P. Lightman, R. V. Wagoner, and C. M. Will, Phys. Rev. Lett. 30, 884 (1973); D. M. Eardley, D. L. Lee, A. P. Lightman, Phys. Rev. D 8, 3308 (1973).
147. D. M. Eardley, D. L. Lee, A. P. Lightman, R. V. Wagoner, and C. M. Will, Phys. Rev. Lett. 30, 884 (1973); D. M. Eardley, D. L. Lee, A. P. Lightman, Phys. Rev. D 8, 3308 (1973).
148. R. A. Isaacson, Phys. Rev. 166, 1263 (1968).
149. C. M. Will and K. Nordtvedt, Astrophys. J. 177, 757 (1972); R. W. Hellings and K. Nordtvedt, Phys. Rev. D 7, 3593 (1973). See also C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, England, 1993).
150. C. M. Will and K. Nordtvedt, Astrophys. J. 177, 757 (1972); R. W. Hellings and K. Nordtvedt, Phys. Rev. D 7, 3593 (1973). See also C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, England, 1993).
151. C. M. Will and K. Nordtvedt, Astrophys. J. 177, 757 (1972); R. W. Hellings and K. Nordtvedt, Phys. Rev. D 7, 3593 (1973). See also C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, England, 1993).
152. Models with this kinetic term have been considered in J. W. Moffat, Int. J. Mod. Phys. D 2, 351 (1993); Found. Phys. 23, 411 (1993).
153. Models with this kinetic term have been considered in J. W. Moffat, Int. J. Mod. Phys. D 2, 351 (1993); Found. Phys. 23, 411 (1993).
154. Note that, in a Lorentz-invariant theory only, the effects of the particle transformations considered in this subsection are equivalent in their action on tensor components to certain inverse observer transformations. The Minkowskispacetime transformations (36) then correspond to observer Lorentz transformations to a local frame with an anholonomic basis, and the diffeomorphisms leading to Eq. (38) correspond to working with special relativity in a non-Cartesian basis.
155. This result can be traced to unobservable field redefinitions that eliminate certain coefficients for Lorentz violation. See Refs. [5,7,24] and M. S. Berger and V. A. Kostelecký, Phys. Rev. D 65, 091701(R) (2002); D. Colladay and P. McDonald, J. Math. Phys. (N.Y.) 43, 3554 (2002).
156. This result can be traced to unobservable field redefinitions that eliminate certain coefficients for Lorentz violation. See Refs. [5,7,24] and M. S. Berger and V. A. Kostelecký, Phys. Rev. D 65, 091701(R) (2002); D. Colladay and P. McDonald, J. Math. Phys. (N.Y.) 43, 3554 (2002).
157. O. Bertolami et al., Phys. Lett. B 395, 178 (1997).
158. E. Sezgin and P. van Nieuwenhuizen, Phys. Rev. D 21, 3269 (1980).
159. K. Fukuma, Prog. Theor. Phys. 107, 191 (2002).