  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.
