Gauge (In)variance, Mass and Parity in D=3 Revisited

TL;DR

This paper revisits gauge invariance, mass, and parity in three-dimensional theories, establishing equivalences and differences between gauge-invariant and non-gauge models, with implications for their excitation spectra and interactions.

Contribution

It demonstrates the equivalence of field equations via generalized Stueckelberg invariance and highlights differences in interaction behaviors, especially in tensor cases, compared to previous theories.

Findings

Equivalent field equations for gauge-invariant and non-gauge models.

Spectral and interaction similarities between models.

Differences in Einstein limit interactions, avoiding known discontinuities.

Abstract

We analyze the degree of equivalence between abelian topologically massive, gauge-invariant, vector or tensor parity doublets and their explicitly massive, non-gauge, counterparts. We establish equivalence of field equations by exploiting a generalized Stueckelberg invariance of the gauge systems. Although the respective excitation spectra and induced source-source interactions are essentially identical, there are also differences, most dramatic being those between the Einstein limits of the interactions in the tensor case: the doublets avoid the discontinuity (well-known from D=4) exhibited by Pauli-Fierz theory.