Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions
A generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and Hilbert spaces. We then relate both the Dirac and Majorana typ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321000122 |
| _version_ | 1818672470961422336 |
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| author | Rohan Pramanick Swarup Sangiri Utpal Sarkar |
| author_facet | Rohan Pramanick Swarup Sangiri Utpal Sarkar |
| author_sort | Rohan Pramanick |
| collection | DOAJ |
| description | A generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and Hilbert spaces. We then relate both the Dirac and Majorana type Bargmann invariants to the rephasing invariant measures of CP violation with the Majorana neutrinos, assuming that the neutrinos have lepton number violating Majorana masses. We then generalize the recursive parametrization for studying any unitary matrices to include the Majorana fermions, which could be useful for studying the neutrino mixing matrix. |
| first_indexed | 2024-12-17T07:40:25Z |
| format | Article |
| id | doaj.art-5880328fdfaf47baae5f80df8fec55ff |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-17T07:40:25Z |
| publishDate | 2021-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-5880328fdfaf47baae5f80df8fec55ff2022-12-21T21:58:10ZengElsevierNuclear Physics B0550-32132021-03-01964115315Bargmann invariants, geometric phases and recursive parametrization with Majorana fermionsRohan Pramanick0Swarup Sangiri1Utpal Sarkar2Corresponding authors.; Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaDepartment of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaCorresponding authors.; Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaA generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and Hilbert spaces. We then relate both the Dirac and Majorana type Bargmann invariants to the rephasing invariant measures of CP violation with the Majorana neutrinos, assuming that the neutrinos have lepton number violating Majorana masses. We then generalize the recursive parametrization for studying any unitary matrices to include the Majorana fermions, which could be useful for studying the neutrino mixing matrix.http://www.sciencedirect.com/science/article/pii/S0550321321000122 |
| spellingShingle | Rohan Pramanick Swarup Sangiri Utpal Sarkar Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions Nuclear Physics B |
| title | Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions |
| title_full | Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions |
| title_fullStr | Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions |
| title_full_unstemmed | Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions |
| title_short | Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions |
| title_sort | bargmann invariants geometric phases and recursive parametrization with majorana fermions |
| url | http://www.sciencedirect.com/science/article/pii/S0550321321000122 |
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