Stochastic Quantization of $(\lambda {\varphi }^4{)}_d$ Scalar Theory: Generalized Langevin Equation with Memory Kernel

Abstract

We review the method of stochastic quantization for a scalar field theory. We first give a brief survey for the case of self-interacting scalar fields, implementing the stochastic perturbation theory up to the one-loop level. The divergences therein are taken care of by employing the usual prescription of the stochastic regularization, introducing a colored random noise in the Einstein relations. We then extend this formalism to the case where we assume a Langevin equation with a memory kernel. We have shown that, if we also maintain the Einstein's relations with a colored noise, there is convergence to a non-regularized theory.

25 pages

References in corpus (4)

• Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• The Two-loop Massless phi^4 Model in Non-translational Invariant Domain
• Finite Size Effects in Thermal Field Theory

Cited by in corpus (6)

• Stochastic Quantization of Scalar Fields in de Sitter Spacetime
• Stochastic Quantization of Scalar Fields in Einstein and Rindler Spacetime
• Stochastic Quantization for Complex Actions
• Stochastic Quantization of Real-Time Thermal Field Theory
• Correlation Functions and Stochastic Feynman Rules for Self-Interacting Scalar Fields
• Markovian versus non-Markovian stochastic quantization of a complex-action model