Remarks on Gauge-Invariant Variables and Interaction Energy in QED

TL;DR

This paper re-examines the calculation of interaction energy in QED and Maxwell-Chern-Simons theories using gauge-invariant variables, highlighting subtleties in explicit energy expressions within a specific gauge.

Contribution

It provides a detailed analysis of gauge-invariant variables and their role in calculating interaction energies in gauge theories, focusing on the Poincaré gauge.

Findings

Clarifies the role of gauge-invariant variables in interaction energy calculations.

Highlights subtleties in explicit energy expressions in specific gauges.

Provides insights into the path dependence formalism in gauge theories.

Abstract

The calculation of the interaction energy in pure QED and Maxwell-Chern-Simons gauge theory is re-examined by exploiting the path dependence of the gauge-invariant variables formalism. In particular, we consider a spacelike straight line which leads to the Poincar\'{e} gauge. Subtleties related to the problem of exhibiting explicitly the interaction energies are illustrated.