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

Zhi Xiao, Bing Sun, Tao Zhu

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.

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

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.
Paper Structure (13 sections, 88 equations, 1 figure, 1 table)

This paper contains 13 sections, 88 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. LI Null formalism and Maxwell equations
  3. Preliminary of null formalism
  4. Null projection of LI Maxwell equations
  5. the intrinsic derivative approach
  6. The differential form approach
  7. The extensions of Maxwell equations in Null formalism
  8. The CPT-odd MCS/CFJ theory
  9. A CPT-even anisotropic extension
  10. The Myers-Pospelov extension
  11. High derivative electrodynamics
  12. The extended operator construction -- a short summary
  13. Summary

Figures (1)

  • Figure 1: Rays in a linearized radiation field. Figure is copied from the Ref. Sachs1960s. In this figure, $k^a$ is denoted as the first null vector $l^\mu$, $v(x)$ is the affine parameter $r$, and $z^a[r^s(x)]$ is the source world line with four-velocity $e^a=dz^a/ds$.