Stochastic quantization for complex actions

We use the stochastic quantization method to study systems with complex valued path integral weights. We assume a Langevin equation with a memory kernel and Einstein’s relations with colored noise. The equilibrium solution of this non-Markovian Langevin equation is analyzed. We show that for a large class of elliptic non-Hermitian operators acting on scalar functions on Euclidean space, which define different models in quantum field theory, converge to an equilibrium state in the asymptotic limit of the Markov parameter $τ→∞$⁠. Moreover, as we expected, we obtain the Schwinger functions of the theory.