Ghost busting: PT-symmetric interpretation of the Lee model

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 2, 2005, Pages

  Bender, Carl M ^a   Brandt, Sebastian F ^a   Chen, Jun Hua ^a   Wang, Qinghai ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; FERMION; LEE MODEL; MATHEMATICAL ANALYSIS; PARAMETER; QUANTUM THEORY; THEORETICAL MODEL;

EID: 84927760893     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.025014     Document Type: Article

References (27)

1. T. D. Lee, Phys. Rev. 95, 1329 (1954).
2. G. Källén and W. Pauli, Dan. Mat.-Fys. Medd. 30, 7 (1955).
3. S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson and Co., Evanston, 1961), Chap. 12.
4. G. Barton, Introduction to Advanced Field Theory (John Wiley & Sons, New York, 1963), Chap. 12.
5. S. Weinberg, Phys. Rev. 102, 285 (1956).
6. R. D. Amado, Phys. Rev. 122, 696 (1961).
7. M. T. Vaughn, Nuovo Cimento 40, 803 (1965).
8. V. Glaser and G. Källén, Nucl. Phys. 2, 706 (1956).
9. C. M. Bender and C. Nash, Phys. Rev. D 10, 1753 (1974).
10. H. D. I. Abarbanel, J. D. Bronzan, R. L. Sugar, and A. R. White, Phys. Rep. 21, 119 (1975); R. Brower, M. Furman, and M. Moshe, Phys. Lett. 76B, 213 (1978); B. Harms, S. Jones, and C.-I. Tan, Nucl. Phys. B171, 392 (1980); Phys. Lett. 91B, 291 (1980).
11. H. D. I. Abarbanel, J. D. Bronzan, R. L. Sugar, and A. R. White, Phys. Rep. 21, 119 (1975); R. Brower, M. Furman, and M. Moshe, Phys. Lett. 76B, 213 (1978); B. Harms, S. Jones, and C.-I. Tan, Nucl. Phys. B171, 392 (1980); Phys. Lett. 91B, 291 (1980).
12. H. D. I. Abarbanel, J. D. Bronzan, R. L. Sugar, and A. R. White, Phys. Rep. 21, 119 (1975); R. Brower, M. Furman, and M. Moshe, Phys. Lett. 76B, 213 (1978); B. Harms, S. Jones, and C.-I. Tan, Nucl. Phys. B171, 392 (1980); Phys. Lett. 91B, 291 (1980).
13. H. D. I. Abarbanel, J. D. Bronzan, R. L. Sugar, and A. R. White, Phys. Rep. 21, 119 (1975); R. Brower, M. Furman, and M. Moshe, Phys. Lett. 76B, 213 (1978); B. Harms, S. Jones, and C.-I. Tan, Nucl. Phys. B171, 392 (1980); Phys. Lett. 91B, 291 (1980).
14. M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978); J. L. Cardy, Phys. Rev. Lett. 54, 1354 (1985); J. L. Cardy and G. Mussardo, Phys. Ltt. B 225, 275 (1989); A. B. Zamolodchikov, Nucl. Phys. B348, 619 (1991).
15. M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978); J. L. Cardy, Phys. Rev. Lett. 54, 1354 (1985); J. L. Cardy and G. Mussardo, Phys. Ltt. B 225, 275 (1989); A. B. Zamolodchikov, Nucl. Phys. B348, 619 (1991).
16. M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978); J. L. Cardy, Phys. Rev. Lett. 54, 1354 (1985); J. L. Cardy and G. Mussardo, Phys. Ltt. B 225, 275 (1989); A. B. Zamolodchikov, Nucl. Phys. B348, 619 (1991).
17. M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978); J. L. Cardy, Phys. Rev. Lett. 54, 1354 (1985); J. L. Cardy and G. Mussardo, Phys. Ltt. B 225, 275 (1989); A. B. Zamolodchikov, Nucl. Phys. B348, 619 (1991).
18. C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
19. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 270401 (2002); Am. J. Phys. 71, 1095 (2003).
20. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 270401 (2002); Am. J. Phys. 71, 1095 (2003).
21. C. M. Bender, P. N. Meisinger, and Q. Wang, J. Phys. A 36, 1973 (2003); C. M. Bender, J. Brod, A. T. Refig, and M. E. Reuter, J. Phys. A 37, 10139 (2004).
22. C. M. Bender, P. N. Meisinger, and Q. Wang, J. Phys. A 36, 1973 (2003); C. M. Bender, J. Brod, A. T. Refig, and M. E. Reuter, J. Phys. A 37, 10139 (2004).
23. C. M. Bender and H. F. Jones, Phys. Lett. A 328, 102 (2004).
24. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 70, 025001 (2004).
25. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 93, 251601 (2004).
26. F. Kleefeld, hep-th/0408028; hep-th/0408097.
27. In previous works on PT symmetry, it is assumed that in order to construct the C operator the theory must have an unbroken PT symmetry. However, in the quantum-mechanical Lee model it is clear that the PT symmetry is broken because for sufficiently many θ quanta there exist sectors in the Hilbert space whose energy eigenvalues are complex. Presumably, such sectors also exist in the quantum-field-theoretic Lee model. Fortunately, the strict decomposition of the Hilbert space into decoupled sectors allows us to establish unitarity in the crucial V/Nθ sector. We assume that the underlying reason for the breaking of PT symmetry is the violation of crossing symmetry. Note that this violation gives rise to a nonlocal interaction term in the Hamiltonian for the quantum-field-theoretic Lee model.