Gauge Invariant Propagators and States in Quantum Electrodynamics

TL;DR

This paper investigates gauge invariant states and propagators in QED, analyzing boundary conditions and large gauge transformations, and demonstrating how Coulombic and soft-photon dressings naturally emerge without gauge fixing.

Contribution

It introduces a boundary-based framework for gauge invariant states in QED, including large gauge transformations and boundary dressings, without fixing a gauge.

Findings

Path integral generates Coulomb-field dressing factors naturally.

Boundary conditions determine the form of the dressing.

Dressing includes Coulombic and soft-photon components at null infinity.

Abstract

We study gauge invariant states in QED, where states are understood in terms of data living on the boundary of gauge invariant path-integrals. This is done for both scalar and spinor QED, and for boundaries that are either time slices, or the boundaries of a 'causal diamond'. We discuss both the case where the gauge field falls off to zero at the boundaries, and the case of 'large gauge transformations', where it remains finite at the boundaries. The dynamics are discussed using the gauge-invariant propagator, describing motion of both the particles and the field between the boundaries. We demonstrate how the path-integral naturally generates a 'Coulomb-field' dressing factor for states living on time-slices, and how this is done without fixing any gauge. We show that the form of the dressing depends only on the nature of the boundaries. We also derive the analogous dressing for states defined on null infinity, showing both its Coulombic parts as well as soft-photon parts.