Stochastic Quantization of Real-Time Thermal Field Theory

TL;DR

This paper applies stochastic quantization methods to derive the finite temperature scalar propagator in Minkowski spacetime, exploring both Markovian and non-Markovian approaches with potential applications to non-equilibrium systems.

Contribution

It introduces a novel stochastic quantization framework for finite temperature field theories, including colored noise and memory effects, extending previous methods.

Findings

Convergence of stochastic processes demonstrated for free scalar theory.

Formulation of Langevin equations with memory kernels and colored noise.

Potential application to non-equilibrium finite temperature systems.

Abstract

We use the stochastic quantization method to obtain the free scalar propagator of a finite temperature field theory formulated in Minkowski spacetime. First we use the Markovian stochastic quantization approach to present the two-point function of the theory. Second, we assume a Langevin equation with a memory kernel and Einstein's relations with colored noise. The convergence of the stochastic processes in the asymptotic limit of the Markov parameter of these Markovian and non-Markovian Langevin equations for a free scalar theory is obtained. Our formalism can be the starting point to discuss systems at finite temperature out of equilibrium.