Mass generation for abelian spin-1 particles via a symmetric tensor

TL;DR

This paper explores a novel mechanism for giving mass to abelian spin-1 particles by coupling them to a symmetric tensor, resulting in a gauge-invariant model without the need for a Higgs field.

Contribution

It introduces a new dual model where the photon gains mass via a symmetric tensor coupling, extending the topologically massive BF framework.

Findings

Massive photon model with symmetric tensor coupling

U(1) gauge symmetry preserved without Higgs field

Explicit symmetry removal via field redefinition

Abstract

In the topologically massive BF model (TMBF) the photon becomes massive via coupling to an antisymmetric tensor, without breaking the U(1) gauge symmetry . There is no need of a Higgs field. The TMBF model is dual to a first-order (in derivatives) formulation of the Maxwell-Proca theory where the antisymmetric field plays the role of an auxiliary field. Since the Maxwell-Proca theory also admits a first-order version which makes use of an auxiliary symmetric tensor, we investigate here a possible generalization of the TMBF model where the photon acquires mass via coupling to a symmetric tensor. We show that it is indeed possible to build up dual models to the Maxwell-Proca theory where the U(1) gauge symmetry is manifest without Higgs field, but after a local field redefinition the vector field eats up the trace of the symmetric tensor and becomes massive. So the explicit U(1) symmetry can be removed unlike the TMBF model.