Vacuum Polarization Effects in the Lorentz and PCT Violating Electrodynamics

TL;DR

This paper investigates how Lorentz and PCT symmetry violations affect vacuum polarization in quantum electrodynamics, exploring dynamical mass generation, gauge invariance, and potential observable effects like photon mass shifts and the Lamb shift.

Contribution

It provides a second-order calculation of vacuum polarization in Lorentz and PCT violating QED, restoring gauge invariance and analyzing physical consequences.

Findings

Gauge invariance is restored at second order in Lorentz violation.

Possible photon mass shifts are discussed.

Observable effects like the Lamb shift are analyzed.

Abstract

In this work we report new results concerning the question of dynamical mass generation in the Lorentz and PCT violating quantum electrodynamics. A one loop calculation for the vacuum polarization tensor is presented. The electron propagator, "dressed" by a Lorentz breaking extra term in the fermion Lagrangian density, is approximated by its first order: this scheme is shown to break gauge invariance. Then we rather consider a full calculation to second order in the Lorentz breaking parameter: we recover gauge invariance and use the Schwinger-Dyson equation to discuss the full photon propagator. This allows a discussion on a possible photon mass shift as well as measurable, observable physical consequences, such as the Lamb-shift.