Radiative corrections in bumblebee electrodynamics

TL;DR

This paper explores quantum aspects of bumblebee electrodynamics, revealing that one-loop corrections do not generate a mass term, but the longitudinal mode's propagation remains possible, indicating complex Lorentz symmetry breaking effects.

Contribution

It provides a detailed analysis of quantum corrections in bumblebee electrodynamics, highlighting the non-transversality of the self-energy and the stability of the photon-like excitation.

Findings

No one-loop radiative corrections to the mass term are generated.

The bumblebee self-energy is not transverse.

The longitudinal mode propagation cannot be excluded.

Abstract

We investigate some quantum features of the bumblebee electrodynamics in flat spacetimes. The bumblebee field is a vector field that leads to a spontaneous Lorentz symmetry breaking. For a smooth quadratic potential, the massless excitation (Nambu-Goldstone boson) can be identified as the photon, transversal to the vacuum expectation value of the bumblebee field. Besides, there is a massive excitation associated with the longitudinal mode and whose presence leads to instability in the spectrum of the theory. By using the principal-value prescription, we show that no one-loop radiative corrections to the mass term is generated. Moreover, the bumblebee self-energy is not transverse, showing that the propagation of the longitudinal mode can not be excluded from the effective theory.