Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
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 L...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/10/1197 |
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| author | João Alfíeres Andrade de Simões dos Reis Marco Schreck |
| author_facet | João Alfíeres Andrade de Simões dos Reis Marco Schreck |
| author_sort | João Alfíeres Andrade de Simões dos Reis |
| collection | DOAJ |
| description | 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 <i>N</i> 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 <i>N</i>, 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. |
| first_indexed | 2024-04-13T08:31:45Z |
| format | Article |
| id | doaj.art-ecefbd845c294c9a851f12280fbbc8aa |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:31:45Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ecefbd845c294c9a851f12280fbbc8aa2022-12-22T02:54:15ZengMDPI AGSymmetry2073-89942019-09-011110119710.3390/sym11101197sym11101197Formal Developments for Lorentz-Violating Dirac Fermions and NeutrinosJoão Alfíeres Andrade de Simões dos Reis0Marco Schreck1Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, São Luís–MA 65080-805, BrazilDepartamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, São Luís–MA 65080-805, BrazilThe 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 <i>N</i> 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 <i>N</i>, 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.https://www.mdpi.com/2073-8994/11/10/1197Lorentz and <i>CPT</i> violationStandard-Model ExtensionDirac fermionsDirac neutrinosMajorana neutrinosdeterminants of block matrices |
| spellingShingle | João Alfíeres Andrade de Simões dos Reis Marco Schreck Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos Symmetry Lorentz and <i>CPT</i> violation Standard-Model Extension Dirac fermions Dirac neutrinos Majorana neutrinos determinants of block matrices |
| title | Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos |
| title_full | Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos |
| title_fullStr | Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos |
| title_full_unstemmed | Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos |
| title_short | Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos |
| title_sort | formal developments for lorentz violating dirac fermions and neutrinos |
| topic | Lorentz and <i>CPT</i> violation Standard-Model Extension Dirac fermions Dirac neutrinos Majorana neutrinos determinants of block matrices |
| url | https://www.mdpi.com/2073-8994/11/10/1197 |
| work_keys_str_mv | AT joaoalfieresandradedesimoesdosreis formaldevelopmentsforlorentzviolatingdiracfermionsandneutrinos AT marcoschreck formaldevelopmentsforlorentzviolatingdiracfermionsandneutrinos |