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

TL;DR

This paper derives explicit solutions for the modified Dirac equation with spin-nondegenerate Lorentz-violating operators in the SME, providing foundational results for future quantum field theory phenomenology involving Lorentz violation.

Contribution

It provides the first explicit derivations of propagators, energies, and spinor solutions for spin-nondegenerate SME fermion operators, including nonminimal cases.

Findings

Derived propagators, energies, and solutions for spin-nondegenerate operators.

Confirmed consistency with the optical theorem at first order.

Established matrices from spinors and conjugates at all orders in Lorentz violation.

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.