On the photon mass generation in Rarita–Schwinger QED

Abstract This work examines the dynamical mass generation for the photon in Rarita–Schwinger QED. We focus our attention on the cases of $$\omega =2,3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> 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 1PI function $$\langle AA \rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mi>A</mml:mi> <mml:mi>A</mml:mi> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> 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.