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Alternative classical Lagrangians for the Standard-Model Extension

João A. A. S. Reis, Marco Schreck, Ronaldo Thibes

Abstract

The current paper introduces classical, relativistic Lagrangians for point-particle analogs to the field theory description of the Standard-Model Extension (SME) for Lorentz violation. Lagrangians of a form alternative to those derived and studied in previous works are in the spotlight. Interestingly, they have well-defined massless limits, which makes them suitable for describing classical-particle analogs of photons subject to Lorentz violation. We first deal with different types of Dirac fermion coefficients, followed by various configurations of the SME photon sector. The Lagrangians are accompanied by constraints that we treat properly using the techniques due to Dirac. The results encountered may find application in photon propagation through gravitational fields in the presence of spacetime symmetry violation. Connections to Finsler geometry are likely to exist.

Alternative classical Lagrangians for the Standard-Model Extension

Abstract

The current paper introduces classical, relativistic Lagrangians for point-particle analogs to the field theory description of the Standard-Model Extension (SME) for Lorentz violation. Lagrangians of a form alternative to those derived and studied in previous works are in the spotlight. Interestingly, they have well-defined massless limits, which makes them suitable for describing classical-particle analogs of photons subject to Lorentz violation. We first deal with different types of Dirac fermion coefficients, followed by various configurations of the SME photon sector. The Lagrangians are accompanied by constraints that we treat properly using the techniques due to Dirac. The results encountered may find application in photon propagation through gravitational fields in the presence of spacetime symmetry violation. Connections to Finsler geometry are likely to exist.
Paper Structure (25 sections, 143 equations, 2 tables)

This paper contains 25 sections, 143 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Lorentz-invariant case
  3. Constraints
  4. Lorentz-violating regime
  5. Massive classical-particle analogs
  6. Coefficients $a_{\mu}$
  7. Coefficients $e_{\mu}$
  8. Coefficients $b_{\mu}$
  9. Coefficients $H_{\mu\nu}$
  10. Additional remarks
  11. Dirac-Bergmann Constraint Analysis
  12. Coefficients $a_{\mu}$
  13. Coefficients $b_{\mu}$
  14. Massless classical-particle analogs
  15. Degenerate quadratic dispersion
  16. ...and 10 more sections