Gauge invariance of relativistic two-particle bound-state energies: (II). Invariant subsets in perturbation theory

Abstract

The gauge invariance, in quantum electrodynamics, of the bound-state energies is proven, order by order in perturbation theory, in the case of solutions of the Beth-Selpeter equation for the spin- 1 2 fermion-antifermion system. A simple algebraic, and corresponding diagrammatic, procedure is developed to deal with the problem. It is shown that subsets of energy contributions are gauge invariant, a property which can provide a useful flexibility in calculations.