Duality and bosonization in Schwinger-Keldysh formulation

TL;DR

This paper develops a path-integral bosonization method for non-equilibrium systems using duality transformations and the Schwinger-Keldysh technique, providing exact results in two dimensions and connecting fermionic and bosonic distributions.

Contribution

It introduces a duality-based bosonization approach applicable to non-equilibrium systems in any dimension, with exact solutions in two dimensions.

Findings

Derived bosonization rules for fermion currents

Calculated current-current correlation functions

Established connection between fermionic and bosonic distribution functions

Abstract

We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for $D \geq 2$ space-time dimensions leading for $D=2$ to exact results. In this last case we present the bosonization rules for fermion currents, calculate current-current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, nonequilibrium situation.