Gauge propagator and physical consistency of the CPT-even part of the Standard Model Extension

TL;DR

This paper evaluates the gauge propagator of the CPT-even part of the Standard Model Extension in electrodynamics, analyzing stability, causality, and unitarity of physical modes in different sectors.

Contribution

It provides explicit calculations of the gauge propagator for the CPT-even SME, analyzing physical consistency in parity-odd and parity-even sectors with specific parametrizations.

Findings

Parity-odd sector modes are stable, non-causal, and unitary.

Parity-even sector modes are causal, stable, and unitary within a limited parameter range.

The work clarifies physical properties of SME modifications to Maxwell theory.

Abstract

In this work, we explicitly evaluate the gauge propagator of the Maxwell theory supplemented by the CPT-even term of the SME. First, we specialize our evaluation for the parity-odd sector of the tensor $W_{\mu \nu \rho \sigma}$,\ using a parametrization that retains only the three nonbirefringent coefficients. From the poles of the propagator, it is shown that physical modes of this electrodynamics are stable, non-causal and unitary. In the sequel, we carry out the parity-even gauge propagator using a parametrization that allows to work with only the isotropic nonbirefringent element. In this case, we show that the physical modes of the parity-even sector of the tensor $W$ are causal, stable and unitary for a limited range of the isotropic coefficient.