Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions
A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/7/1144 |
| _version_ | 1797563038951276544 |
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| author | Avraham Nofech |
| author_facet | Avraham Nofech |
| author_sort | Avraham Nofech |
| collection | DOAJ |
| description | A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary. |
| first_indexed | 2024-03-10T18:36:54Z |
| format | Article |
| id | doaj.art-c717143654d34d05af5617bc4796bcef |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T18:36:54Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c717143654d34d05af5617bc4796bcef2023-11-20T06:11:59ZengMDPI AGSymmetry2073-89942020-07-01127114410.3390/sym12071144Biquaternionic Dirac Equation Predicts Zero Mass for Majorana FermionsAvraham Nofech0Department of Mathematics and Statistics, MacEwan University, Edmonton, AB T5J 4S2, CanadaA biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary.https://www.mdpi.com/2073-8994/12/7/1144Dirac EquationbiquaternionMajoranamassPauli algebraouter automorphism |
| spellingShingle | Avraham Nofech Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions Symmetry Dirac Equation biquaternion Majorana mass Pauli algebra outer automorphism |
| title | Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions |
| title_full | Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions |
| title_fullStr | Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions |
| title_full_unstemmed | Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions |
| title_short | Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions |
| title_sort | biquaternionic dirac equation predicts zero mass for majorana fermions |
| topic | Dirac Equation biquaternion Majorana mass Pauli algebra outer automorphism |
| url | https://www.mdpi.com/2073-8994/12/7/1144 |
| work_keys_str_mv | AT avrahamnofech biquaternionicdiracequationpredictszeromassformajoranafermions |