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arXiv · 2301.06703

Non-Gaussianity from Schwinger-Keldysh Effective Field Theory

Shu Lin·Yanyan Bu·Chang Lei
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Abstract

We present a systematic treatment of non-Gaussianity in stochastic systems using the Schwinger-Keldysh effective field theory framework, in which the non-Gaussianity is realized as nonlinear terms in the fluctuation field. We establish two stochastic formulations of the Schwinger-Keldysh effective field theory, with those nonlinear terms manifested as multiple non-Gaussian noises in the Langevin equation and as higher order diffusive terms in the Fokker-Planck equation. The equivalence of the stochastic formulations with the original Schwinger-Keldysh effective field theory is demonstrated with non-trivial examples for arbitrary non-Gaussian parameters. The stochastic formulations will be more flexible and effective in studying non-equilibrium dynamics. We also reveal an ambiguity when coarse-graining time scale and non-Gaussian parameters vanish simultaneously, which may be responsible for the unphysical divergence found in perturbative analysis.

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Shu Lin, Yanyan Bu, Chang Lei. 2023-01-17. Non-Gaussianity from Schwinger-Keldysh Effective Field Theory. https://arxiv.org/abs/2301.06703

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