Non-Gaussianity from Schwinger-Keldysh effective field theory

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 nontrivial examples for arbitrary non-Gaussian parameters. The stochastic formulations will be more flexible and effective in studying nonequilibrium dynamics. We also reveal an ambiguity when coarse-graining timescale and non-Gaussian parameters vanish simultaneously, which may be responsible for the unphysical divergence found in perturbative analysis.