Maxwell theories along the light track: Null Formalism in extended electrodynamics

TL;DR

This paper introduces a differential-form method combined with Newman-Penrose formalism to analyze Lorentz-violating extensions of Maxwell electrodynamics, providing a systematic, coordinate-independent approach for studying photon behavior.

Contribution

It develops a novel differential-form framework to derive null-tetrad equations for extended Maxwell theories, simplifying the analysis of Lorentz-violating effects.

Findings

Provides a compact, gauge-invariant action construction up to mass dimension six.

Enables systematic analysis of photon propagation and polarization in Lorentz-violating scenarios.

Offers an efficient tool for future theoretical and phenomenological studies.

Abstract

We develop a differential-form approach to systematically derive the Newman-Penrose null-tetrad equations for Lorentz-violating extensions of Maxwell electrodynamics. The coordinate-independent nature of differential forms allows the actions and corresponding field equations of the theory to be expressed compactly and enables a systematic and transparent derivation of first-order equations in the Newman-Penrose formalism. Within this formalism, we explicitly present a simple algebraic construction for the gauge invariant extended Maxwell actions that avoids explicit index manipulations up to mass dimension six. The combined scheme of differential-form approach and Newman-Penrose formalism offers an efficient tool for analyzing Lorentz-violating effects on asymptotic photon propagation and polarization.