Gauge covariant formulation of Wigner representation through deformational quantization --Application to Keldysh formalism with electromagnetic field--

TL;DR

This paper introduces a gauge-covariant Wigner representation using deformational quantization to improve calculations of gauge-invariant observables in non-equilibrium Green functions under electromagnetic fields.

Contribution

It develops a novel gauge-covariant formulation of the non-equilibrium Green function method using star products in Wigner space, enabling systematic gauge-invariant calculations.

Findings

Facilitates order-by-order gauge-invariant calculations

Applied to linear response theory with electromagnetic fields

Enhances non-equilibrium Green function analysis

Abstract

We developed a gauge-covariant formulation of the non-equilibrium Green function method for the dynamical and/or non-uniform electromagnetic field by means of the deformational quantization method. Such a formulation is realized by replacing the Moyal product in the so-called Wigner space by the star product, and facilitates the order-by-order calculation of a gauge-invariant observable in terms of the electromagnetic field. An application of this formalism to the linear response theory is discussed.