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

Author

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  • Menezes, G.
  • Svaiter, N.F.

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.

Suggested Citation

  • Menezes, G. & Svaiter, N.F., 2007. "Stochastic quantization of (λϕ4)d scalar theory: Generalized Langevin equation with memory kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 617-630.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:2:p:617-630
    DOI: 10.1016/j.physa.2006.07.038
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