Solvable Models Of Infrared Gupta-Bleuler Quantum Electrodynamics

TL;DR

This paper compares solvable infrared models of Gupta-Bleuler QED in different gauges, analyzing their infrared contributions and demonstrating how to avoid spurious effects through specific approximations and expansions.

Contribution

It provides explicit solvable models for infrared QED, compares gauge-dependent infrared effects, and shows how to eliminate spurious contributions with a refined expansion method.

Findings

Infrared models in Coulomb and Feynman gauges are explicitly constructed.

Spurious infrared contributions arise in Feynman's gauge with dipole approximation.

Dropping the dipole approximation and using a fixed momentum expansion reproduces standard infrared behavior.

Abstract

Hamiltonian models based on two different infrared approximations are studied in order to obtain an explicit comparison with the standard analysis of the infrared contributions, occurring in the relativistically covariant perturbative formulation of Quantum Electrodynamics. Moller operators, preserving respectively the Hilbert scalar product, for the Coulomb-gauge models, and an indefinite metric, for the models formulated in Feynman's gauge, are obtained in the presence of an infrared cutoff, after the removal of an adiabatic switching and with the aid of a suitable mass renormalization. In the presence of a dipole approximation, spurious contributions to the infrared factors are shown to necessarily arise in Feynman's gauge, with respect both to the Coulomb-gauge model and to the amplitudes of Quantum Electrodynamics, and the connection of this result with a recent work on the Gupta-Bleuler formulation of non-relativistic models is discussed. It is finally proven that by dropping the dipole approximation and adopting an expansion around a fixed charged particle four-momentum, first introduced and employed in the study of the infrared problem by Bloch and Nordsieck, the infrared diagrammatic is fully reproduced and spurious low-energy effects are avoided.