publication . Preprint . Article . 1996

Nonperturbative calculation of symmetry breaking in quantum field theory

Kimball A. Milton; Carl M. Bender;
Open Access English
  • Published: 08 Aug 1996
Abstract
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the expectation value of the scalar field to first order in delta, where delta is a measure of the degree of nonlinearity in the interaction term.
Subjects
free text keywords: High Energy Physics - Theory, Nonlinear system, Scalar field, Scalar (physics), Expectation value, Quantum mechanics, First order, Symmetry breaking, Physics, Quantum field theory

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.

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