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PT-Symmetric Quantum Field Theories and the Langevin Equation

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Czechoslovak Journal of Physics Aims and scope

Abstract

Many non-Hermitian but PT-symmetric theories are known to have a real, positive spectrum, and for quantum-mechanical versions of these theories, there exists a consistent probabilistic interpretation. Since the action is complex for these theories, Monte Carlo methods do not apply. In this paper a field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point 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. This approach may grant insight into the formulation of a probabilistic interpretation for path integrals in PT-symmetric quantum field theories.

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Authors and Affiliations

  1. Department of Physics, Washington University, St. Louis, Missouri, 63130, USA

    Claude Bernard

  2. The Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA

    Van M. Savage

  3. Theoretical Division, MSB285, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Van M. Savage

Authors
  1. Claude Bernard
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  2. Van M. Savage
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Bernard, C., Savage, V.M. PT-Symmetric Quantum Field Theories and the Langevin Equation. Czechoslovak Journal of Physics 54, 109–118 (2004). https://doi.org/10.1023/B:CJOP.0000014375.58419.0d

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  • DOI: https://doi.org/10.1023/B:CJOP.0000014375.58419.0d

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