Wigner-Moyal description of free variable mass Klein-Gordon fields

TL;DR

This paper derives a set of coupled kinetic equations for the Wigner distributions of free variable mass Klein-Gordon fields, enabling analysis of broadband wave interactions and instabilities in nonlinear dispersive media.

Contribution

It introduces a novel Wigner-Moyal formalism for variable mass Klein-Gordon fields, linking quantum field theory with classical wave dynamics in complex media.

Findings

Derivation of coupled kinetic transport equations for Wigner distributions.

Formal equivalence to electromagnetic wave equations in nonlinear media.

Recovery of classical wave action results in the short wavelength limit.

Abstract

A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in nonlinear dispersive media, thus allowing for the description of broadband radiation-matter interactions and the associated instabilities. The standard results for the classical wave action are recovered in the short wavelength limit of the generalized Wigner-Moyal formalism for the wave equation.