Lorentz-violating extension of the spin-one Duffin-Kemmer-Petiau equation

TL;DR

This paper explores how adding a Lorentz-violating Chern-Simons-like term to the Duffin-Kemmer-Petiau equation affects photon propagation, revealing birefringence and new properties of projection operators.

Contribution

It introduces a Lorentz-violating extension to the Duffin-Kemmer-Petiau equation and analyzes its effects on photon behavior and gauge invariance.

Findings

Birefringence appears due to Lorentz violation

New properties of projection operators are derived

Gauge invariance is maintained in the extended model

Abstract

We investigate the breaking of Lorentz symmetry caused by the inclusion of an external four-vector via a Chern-Simons-like term in the Duffin-Kemmer-Petiau Lagrangian for massless and massive spin-one fields. The resulting equations of motion lead to the appearance of birefringence, where the corresponding photons are split into two propagation modes. We discuss the gauge invariance of the extended Lagrangian. Throughout the paper, we utilize projection operators to reduce the wave-functions to their physical components, and we provide many new properties of these projection operators.