Stochastic Quantization for Complex Actions

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.

References in corpus (5)

• Complex Langevin Equations and Schwinger-Dyson Equations
• On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions
• Stochastic Quantization of $(\lambda {\varphi }^4{)}_d$ Scalar Theory: Generalized Langevin Equation with Memory Kernel
• Stochastic Quantization of Scalar Fields in Einstein and Rindler Spacetime
• Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel

Cited by in corpus (4)

• Effective Potential for Complex Langevin Equations
• Stochastic Quantization of Scalar Fields in de Sitter Spacetime
• Stochastic Quantization of Real-Time Thermal Field Theory
• Markovian versus non-Markovian stochastic quantization of a complex-action model