Numerical simulations of PT-symmetric quantum field theories -: art. no. 085010

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.