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arXiv · 1909.11061

Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

J. A. A. S. Reis·M. Schreck
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Abstract

The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of $N$ neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic $N$, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.

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J. A. A. S. Reis, M. Schreck. 2019-09-24. Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos. https://doi.org/10.3390/sym11101197

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