On the photon mass generation in Rarita-Schwinger QED

TL;DR

This paper investigates how Rarita-Schwinger fields influence photon mass generation in QED across 2 and 3 dimensions, highlighting higher-derivative effects and their implications for renormalizability.

Contribution

It provides a detailed analysis of photon mass generation mechanisms in Rarita-Schwinger QED, emphasizing the role of higher-derivative terms at one-loop order.

Findings

Higher-derivative terms dominate the photon self-energy at one-loop.

The photon acquires a gauge-invariant mass in certain dimensions.

Renormalizability is affected by higher-derivative corrections.

Abstract

This work examines the dynamical mass generation for the photon in Rarita-Schwinger QED. We focus our attention on the cases of $\omega=2,3$ dimensional spacetime. In these frameworks, it is well known that in the usual QED, the photon field (dynamically) acquires a gauge invariant mass (the Schwinger and Chern-Simons mass, respectively). We wish to scrutinize this phenomenon in terms of the Rarita-Schwinger fields. The presence of higher-derivative terms is shown as the leading contributions to the $1$PI function $\langle AA \rangle$ at one-loop order. We study the pole structure of the photon's complete propagator to unveil the main effects of the Rarita-Schwinger fields on the photon's mass. In addition, we present some remarks about the renormalizability of this model (in different dimensions) due to the presence of higher-derivative corrections at one-loop.