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

G. Menezes·N. F. Svaiter
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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.

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G. Menezes, N. F. Svaiter. 2005-11-22. Stochastic Quantization of $(λϕ^{4})_d$ Scalar Theory: Generalized Langevin Equation with Memory Kernel. https://doi.org/10.1016/j.physa.2006.07.038

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