Nonperturbative quantization of phantom and ghost theories: Relating definite and indefinite representations

International Journal of Modern Physics A

Volumn 22, Issue 14-15, 2007, Pages 2563-2608

  Van Tonder, André ^a,b   Dorca, Miquel ^a,b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF RHODE ISLAND   (United States)

Author keywords

Ghosts and phantoms; Indefinite inner product representations; Lee Wick theories

Indexed keywords

EID: 34547249780     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0217751x07036580     Document Type: Article

References (37)

1. T. D. Lee and G. C. Wick, Nucl. Phys. B 9, 209 (1969).
2. T. D. Lee, A finite theory of quantum electrodynamics, in Elementary Processes at High Energy, Ettore Majorana 1970 International School of Subnuclear Physics, Part A, Erice, July 1-19, 1970, eds. A. Zichichi (Academic Press, New York and London, 1971).
3. R. E. Cutkosky, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, Nucl. Phys. B 12, 281 (1969).
4. D. G. Boulware and D. G. Gross, Nucl. Phys. B 233, 1 (1984).
5. S. Sakoda, Euclidean path integral of the gauge field - holomorphic representation, hep-th/0501205.
6. I. M. Gel'fand and G. E. Shilov, Generalized Functions: Spaces of Fundamental and Generalized Functions, Vol. 2 (Academic Press, Orlando, 1958).
7. I. M. Gel'fand and G. E. Shilov, Generalized Functions: Theory of Differential Equations, Vol. 3 (Academic Press, Orlando, 1967).
8. H. Arisue, T. Fujiwara, T. Inoue and K. Ogawa, J. Math. Phys. 22, 2055 (1981).
9. R. R. Caldwell, Phys. Lett. B 545, 23 (2002).
10. J. M. Cline, S.-Y. Jeon and G. D. Moore, Phys. Rev. D 70, 043543 (2004).
11. A. De Felice, M. Hindmarsh and M. Trodden, J. Cosmol. Astropart. Phys. 08, 005 (2006).
12. J. Kujat, R. J. Scherrer and A. A. Sen, Phys. Rev. D 74, 083501 (2006), astro-ph/0606735.
13. M. P. Dabrowski, C. Kiefer and B. Sandhoefer, Phys. Rev. D 74, 044022 (2006).
14. R. Erdem, Phys. Lett. B 621, 11 (2005).
15. R. Erdem, Phys. Lett. B 639, 348 (2006).
16. G. 't Hooft and S. Nobbenhuis, Class. Quantum Grav. 23, 3819 (2006).
17. D. E. Kaplan and R. Sundrum, J. High Energy Phys. 0607, 042 (2006).
18. I. Antoniadis, E. Dudas and D. M. Ghilencea, Nucl. Phys. B 767, 29 (2007), hep-th/0608094.
19. W. Pauli and F. Villars, Rev. Mod. Phys. 21, 434 (1949).
20. T. Berggren, Nucl. Phys. A 109, 265 (1968).
21. R. G. Newton, J. Math. Phys. 1, 319 (1960).
22. A. Buchleitner, B. Grémaud and D. Delande, J. Phys. B 27, 2663 (1994).
23. N. Moiseyev, Phys. Rep. 302, 211 (1998).
24. G. Hagen, J. S. Vaagen and M. Hjort-Jensen, J. Phys. A 37, 8991 (2004).
25. Y. K. Ho, Phys. Rep. 99, 1 (1983).
26. R. de la Madrid, AIP Conf. Proc. 885, 3 (2007), quant-ph/0607168.
27. C. M. Bender, S. F. Brandt, J.-H. Chen and Q.-H. Wang, Phys. Rev. D 71, 025014 (2005).
28. J. Bognár, Indefinite Inner Product Spaces (Springer-Verlag, Berlin, 1974).
29. A. I. Mal'cev, Foundations of Linear Algebra (W.H. Freeman and Company, 1963).
30. P. Cartier and C. DeWitt-Morette, A rigorous mathematical foundation of functional integration, in Functional Integration: Basics and Applications - Proc. NATO Advanced Study Institute, Cargese, France, September 1-14 1996, eds. C. DeWitt-Morette, P. Cartier and A. Folacci, (Plenum Press, New York, 1997).
31. G. W. Johnson and M. L. Lapidus, The Feynman Integral and Feynman's Operational Calculus (Oxford University Press, Oxford, 2000).
32. G. Vitali, Rend. R. Istor. Lombardo (2) 36, 772 (1903).
33. G. Vitali, Ann. Mat. Pura Appl. (3) 10, 73 (1904).
34. P. van Nieuwenhuizen and A. Waldron, Phys. Lett. B 389, 29 (1996).
35. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Perseus Books, Cambridge, MA, 1995).
36. N. N. Bogolubov, A. A. Logunov, A. I. Oksak and I. T. Todorov, General Principles of Quantum Field Theory, English edition (Kluwer Academic Publishers, Dordrecht, 1990).
37. A. van Tonder, Int. J. Mod. Phys. A. 21, 6525 (2006), hep-th/0606017.