Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators

Abstract

The Standard-Model Extension (SME) parameterizes all possible Lorentz-violating contributions to the Standard Model and General Relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory.

38 pages, 1 figure

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Cited by in corpus (19)

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• Vacuum Cherenkov radiation for Lorentz-violating fermions
• Thermal aspects of interacting quantum gases in Lorentz-violating scenarios
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Maxwell electrodynamics modified by a CPT-odd dimension-five higher-derivative term
• (Gravitational) Vacuum Cherenkov Radiation
• Dimensional reduction of the electromagnetic sector of the nonminimal Standard-Model-Extension
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• Impact of Lorentz violation on anomalous magnetic moments of charged leptons
• Beta-Decay Spectrum and Lorentz Violation
• Lorentz-violating contributions to the nuclear Schiff moment and nuclear EDM
• Physical interpretation of large Lorentz violation via Weyl semimetals
• Nonperturbative Lorentz Violation and Field Quantization
• Constraining dimension-six nonminimal Lorentz-violating electron-nucleon interactions with EDM physics
• Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
• Lorentz-violating extension of scalar QED at finite temperature
• Re-assessing special aspects of Dirac fermions in presence of Lorentz-symmetry violation
• Tree-level unitarity, causality and higher-order Lorentz and CPT violation
• The analogy of the Lorentz-violating fermion-gravity and fermion photon couplings