Spinorial density matrix equation and gauge covariance

TL;DR

This paper derives a spinorial density matrix equation using Lie group methods in finite-temperature quantum field theory, analyzing its symmetries and gauge covariance, and discusses related Lagrangian formalism and curved space-time extensions.

Contribution

It introduces a novel derivation of the spinorial density matrix equation applying Lie group representations and explores its gauge covariance and symmetry properties.

Findings

One solution is the generalized density matrix operator by Heinz.

The symmetry properties of the derived equation are analyzed.

Preliminary discussion on Lagrangian formalism and curved space-time applications.

Abstract

In this work we apply the Lie group representation method introduced in the real time formalism for finite-temperature quantum-field theory, thermofield dynamics, to derive a spinorial density matrix equation. Symmetry properties of such equation are analysed, and as a basic result it is shown that one solution is the generalised density matrix operator proposed by Heinz, to deal with gauge covariant kinetic equations. In the same context, preliminary aspects of a Lagrangian formalism to derive kinetic equations, as well as quantum density matrix equations in curved space-time, are discussed.