# Nonperturbative calculation of symmetry breaking in quantum field theory

- Published: 08 Aug 1996

- Department of Physics and Astronomy University of California, Irvine United States
- University of Oklahoma United States
- Department of Physics and Astronomy University of Rochester United States

Z[0] J=0

[1] C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., J. Math. Phys. 30, 1447 (1989); C. M. Bender, S. Boettcher, and K. A. Milton, J. Math. Phys. 32, 3031 (1991); B. Abraham-Shrauner, C. M. Bender, and R. N. Zitter, J. Math. Phys. 33, 1335 (1992).

[2] C. M. Bender, K. A. Milton, M. Moshe, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. Lett. 58, 2615 (1987); C. M. Bender, K. A. Milton, M. Moshe, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. D 37, 1472 (1988).

[3] C. M. Bender and H. F. Jones, Phys. Rev. D 38, 2526 (1988); H. T. Cho, K. A. Milton, J. Cline, S. S. Pinsky, and L. M. Simmons, Jr., Nucl. Phys. B 329, 574 (1990).

[4] C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Lett. B 205, 493 (1988); C. M. Bender and K. A. Milton, Phys. Rev. D 38, 1310 (1988).

[5] C. M. Bender, F. Cooper, and K. A. Milton, Phys. Rev. D 40, 1354 (1989); C. M. Bender, S. Boettcher, and K. A. Milton, Phys. Rev. D 45, 639 (1992); C. M. Bender, F. Cooper, K. Milton, M. Moshe, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. D 45, 1248 (1992); C. M. Bender, K. A. Milton, and M. Moshe, Phys. Rev. D 45, 1261 (1992).

[6] C. M. Bender, F. Cooper, and K. A. Milton, Phys. Rev. D 39, 3684 (1989); C. M. Bender, F. Cooper, G. Kilkup, P. Roy, and L. M. Simmons, Jr., J. Stat. Phys. 64, 395 (1991).

[7] C. M. Bender and T. Rebhan, Phys. Rev. D 41, 3269 (1990).

[9] Schwinger-Dyson equations, symmetry breaking, and choice of path integral contour have been studied by S. Garcia and G. S. Guralnik, Proceedings of Workshop on Quantum Infrared Physics, American University of Paris (Paris, France, 6-18 June 1994), World Scientific, p. 205; Z. Guralnik, to be published in the Proceedings of Orbis Scientiae 1996.

[10] E. R. Caianello and G. Scarpetta, Nuovo Cimento 22A, 454 (1974); C. M. Bender and R. Z. Roskies, Phys. Rev. D 25, 427 (1982); C. M. Bender and F. Cooper, Phys. Rev. D 39, 2343 (1989).

[13] Such potentials are described in A. V. Turbiner, Sov. Phys., J. E. T. P. 67, 230 (1988); M. A. Shifman and A. V. Turbiner, Comm. Math. Phys. 126, 347 (1989); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (Institute of Physics, Bristol, 1993) and references therein; A. Krajewska, A. Ushveridze, and Z. Walczak, preprint hep-th/9601088.