On the Physical Propagators of QED

TL;DR

This paper calculates gauge-invariant, infrared-finite propagators for physical variables in QED at one loop, clarifying their behavior and invariance properties.

Contribution

It provides explicit one-loop calculations of physical propagators in QED using physical variables, demonstrating their gauge invariance and infrared finiteness.

Findings

Physical electron propagator is infrared finite in all gauges.

All physical Green's functions are gauge invariant.

Explicit one-loop propagator expressions in terms of physical variables.

Abstract

The true variables in QED are the transverse photon components and Dirac's physical electron, constructed out of the fermionic field and the longitudinal components of the photon. We calculate the propagators in terms of these variables to one loop and demonstrate their gauge invariance. The physical electron propagator is shown not to suffer from infrared divergences in any gauge. In general, all physical Green's functions are gauge invariant and infrared-finite.