Stochastic quantization of (λϕ4)d scalar theory: Generalized Langevin equation with memory kernel

G. Menezes and N.F. Svaiter

Physica A: Statistical Mechanics and its Applications, 2007, vol. 374, issue 2, 617-630

Abstract: The method of stochastic quantization for a scalar field theory is reviewed. A brief survey for the case of self-interacting scalar field, implementing the stochastic perturbation theory up to the one-loop level, is presented. Then, it is introduced a colored random noise in the Einstein's relations, a common prescription employed by one of the stochastic regularizations, to control the ultraviolet divergences of the theory. This formalism is extended to the case where a Langevin equation with a memory kernel is used. It is shown that, maintaining the Einstein's relations with a colored noise, there is convergence to a non-regularized theory.

Keywords: Stochastic quantization; Non-Markovian processes; Stochastic regularization (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:374:y:2007:i:2:p:617-630

DOI: 10.1016/j.physa.2006.07.038

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