Stochastic Quantization for Complex Actions

TL;DR

This paper explores stochastic quantization with memory effects for complex actions, demonstrating convergence to equilibrium and deriving Schwinger functions for non-Hermitian operators in quantum field theory.

Contribution

It introduces a non-Markovian Langevin equation with colored noise for complex actions and proves convergence to equilibrium states for a broad class of operators.

Findings

Convergence to equilibrium in non-Markovian stochastic quantization.

Derivation of Schwinger functions for complex, non-Hermitian operators.

Extension of stochastic quantization methods to systems with memory effects.

Abstract

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, converges to an equilibrium state in the asymptotic limit of the Markov parameter. Moreover, as we expected, we obtain the Schwinger functions of the theory.