2013/08/22 by V. Alan Kostelecký, Alan Kostelecky, Matthew Mewes · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Fermion #Lorentz covariance #Lorentz factor #Lorentz transformation #Mathematical physics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Quantum mechanics #Spinor #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.88.096006
published as Phys.Rev.D88:096006,2013 · 29 pages two-column REVTeX
arxiv created 2013/08/22 · openalex publication_date 2013/11/12 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.