On the occurrence of mass in field theory

TL;DR

This paper demonstrates how to construct a gauge-invariant Lagrangian for quantum electrodynamics that explicitly sets the photon mass to zero, ensuring gauge independence and renormalizability, and explores extensions to non-Abelian theories.

Contribution

It introduces a Lagrangian formulation for QED that makes the photon mass zero explicit and maintains gauge independence, with implications for non-Abelian gauge theories.

Findings

Photon mass can be explicitly set to zero in the Lagrangian.

Gauge independence achieved through gauge-averaging and ghost fields.

Photon propagator behaves as 1/k^2 at high momentum, confirming renormalizability.

Abstract

This paper proves that it is possible to build a Lagrangian for quantum electrodynamics which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. Gauge independence is achieved upon considering the joint effect of gauge-averaging term and ghost fields. It remains possible to obtain a counterterm Lagrangian where the only non-gauge-invariant term is proportional to the squared divergence of the potential, while the photon propagator in momentum space falls off like 1 over (k-squared) at large k, which indeed agrees with perturbative renormalizability. The resulting radiative corrections to the Coulomb potential in QED are also shown to be gauge-independent. The experience acquired with quantum electrodynamics is used to investigate properties and problems of the extension of such ideas to non-Abelian gauge theories.