Classical relativistic systems of charged particles in the front form of dynamics and the Liouville equation

TL;DR

This paper develops a gauge-invariant formulation of relativistic charged particle systems coupled with electromagnetic fields using the front form of dynamics, deriving the Liouville equation for statistical mechanics.

Contribution

It introduces a gauge-invariant approach to relativistic particle-field systems in the front form, applying Dirac's constrained Hamiltonian mechanics to statistical mechanics.

Findings

Derived the classical partition function in a gauge-invariant form

Performed integration over electromagnetic field variables

Applied the Liouville equation to relativistic statistical mechanics

Abstract

Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description is reduced by use of the geometrical concept of the forms of relativistic dynamics. The remainder gauge degrees of freedom of the electromagnetic potential are analysed within the framework of Dirac's constrained Hamiltonian mechanics in the front form of dynamics. The results are implemented to the problems of relativistic statistical mechanics. Based on the corresponding Liouville equation the classical partition function of the system is written down in a gauge-invariant manner and an integration over field variables is performed.