The Stueckelberg Field

TL;DR

The paper reviews the Stueckelberg mechanism, extending it to the standard model to give mass to the photon, discusses its implications, historical influence, and explores potential generalizations to non-Abelian gauge theories.

Contribution

It provides a comprehensive review of the Stueckelberg mechanism's application to the standard model and discusses prospects for extending it beyond Abelian theories.

Findings

Stueckelberg mechanism can give mass to the photon in the standard model.

Neutrinos acquire coupling to the photon through this mechanism.

The Higgs mechanism remains the only known renormalizable way to give mass to non-Abelian gauge fields.

Abstract

In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge theory massive but preserves gauge invariance. The Stueckelberg mechanism is the introduction of new fields to reveal a symmetry of a gauge--fixed theory. We first review the Stueckelberg mechanism in the massive Abelian gauge theory. We then extend this idea to the standard model, stueckelberging the hypercharge U(1) and thus giving a mass to the physical photon. This introduces an infrared regulator for the photon in the standard electroweak theory, along with a modification of the weak mixing angle accompanied by a plethora of new effects. Notably, neutrinos couple to the photon and charged leptons have also a pseudo-vector coupling. Finally, we review the historical influence of Stueckelberg's 1938 idea, which led to applications in many areas not anticipated by the author, such as strings. We describe the numerous proposals to generalize the Stueckelberg trick to the non-Abelian case with the aim to find alternatives to the standard model. Nevertheless, the Higgs mechanism in spontaneous symmetry breaking remains the only presently known way to give masses to non-Abelian vector fields in a renormalizable and unitary theory.