Numerical simulations of PT-symmetric quantum field theories

Claude Bernard and Van M. Savage
Phys. Rev. D 64, 085010 – Published 25 September 2001
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Abstract

Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for these theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which was used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one- and two-point Green’s functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.

  • Received 18 June 2001

DOI:https://doi.org/10.1103/PhysRevD.64.085010

©2001 American Physical Society

Authors & Affiliations

Claude Bernard* and Van M. Savage

  • Department of Physics, Washington University, St. Louis, Missouri 63130

  • *Email address: cb@lump.wustl.edu
  • Email address: vmsavage@hbar.wustl.edu

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Issue

Vol. 64, Iss. 8 — 15 October 2001

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