Numerical Simulations of PT-Symmetric Quantum Field Theories

TL;DR

This paper introduces a novel numerical simulation method for PT-symmetric quantum field theories using the complex Langevin equation, enabling analysis of complex Hamiltonians where traditional Monte Carlo methods fail.

Contribution

First field-theoretic numerical method for PT-symmetric Hamiltonians, utilizing complex Langevin dynamics to overcome complex action challenges.

Findings

Computed Green's functions in 0 and 1 dimensions with results matching known data.

Demonstrated the method's potential applicability in four-dimensional space-time.

Provided insights into probabilistic interpretations of PT-symmetric theories.

Abstract

Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there 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 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. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.