Fermions with Lorentz-violating operators of arbitrary dimension

TL;DR

This paper develops a comprehensive theoretical framework for describing fermions with Lorentz and CPT violation, classifying all possible operators of arbitrary dimension and deriving their physical implications and observational constraints.

Contribution

It provides a complete classification of Lorentz- and CPT-violating operators for fermions of any dimension, including dispersion relations and experimental bounds.

Findings

Derived exact fermion dispersion relations.

Identified observable Lorentz-violating coefficients.

Connected theory to astrophysical constraints.

Abstract

The theoretical description of fermions in the presence of Lorentz and CPT violation is developed. We classify all Lorentz- and CPT-violating and invariant terms in the quadratic Lagrange density for a Dirac fermion, including operators of arbitrary mass dimension. The exact dispersion relation is obtained in closed and compact form, and projection operators for the spinors are derived. The Pauli hamiltonians for particles and antiparticles are extracted, and observable combinations of operators are identified. We characterize and enumerate the coefficients for Lorentz violation for any operator mass dimension via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is presented, including isotropic models, the nonrelativistic and ultrarelativistic limits, and the minimal Standard-Model Extension. Expressions are derived in several limits for the fermion dispersion relation, the associated fermion group velocity, and the fermion spin-precession frequency. We connect the analysis to some other formalisms and use the results to extract constraints from astrophysical observations on isotropic ultrarelativistic spherical coefficients for Lorentz violation.