Non-Gaussianity from Schwinger-Keldysh Effective Field Theory

Understand

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.