Next Article in Journal
A Review of Blockchain Architecture and Consensus Protocols: Use Cases, Challenges, and Solutions
Next Article in Special Issue
Lorentz and CPT Tests Using Penning Traps
Previous Article in Journal
The Circular Hill Problem Regarding Arbitrary Disturbing Forces: The Periodic Solutions that are Emerging from the Equilibria
Previous Article in Special Issue
Lorentz-Violating Matter-Gravity Couplings in Small-Eccentricity Binary Pulsars
Open AccessArticle

Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

1
Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, São Luís–MA 65080-805, Brazil
2
Departamento de Física, Centro de Educação, Ciências Exatas e Naturais, Universidade Estadual do Maranhão, Cidade Universitária Paulo VI, São Luís–MA 65055-310, Brazil
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1197; https://doi.org/10.3390/sym11101197
Received: 31 August 2019 / Revised: 14 September 2019 / Accepted: 17 September 2019 / Published: 24 September 2019
(This article belongs to the Special Issue Symmetry in Special and General Relativity)
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. View Full-Text
Keywords: Lorentz and CPT violation; Standard-Model Extension; Dirac fermions; Dirac neutrinos; Majorana neutrinos; determinants of block matrices Lorentz and CPT violation; Standard-Model Extension; Dirac fermions; Dirac neutrinos; Majorana neutrinos; determinants of block matrices
MDPI and ACS Style

Reis, J.A.A.S.; Schreck, M. Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos. Symmetry 2019, 11, 1197.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop