Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times
Abstract Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoull...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-10853-5 |
| _version_ | 1811182250452058112 |
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| author | Tonatiuh Matos Omar Gallegos Pierre-Henri Chavanis |
| author_facet | Tonatiuh Matos Omar Gallegos Pierre-Henri Chavanis |
| author_sort | Tonatiuh Matos |
| collection | DOAJ |
| description | Abstract Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation. |
| first_indexed | 2024-04-11T09:29:29Z |
| format | Article |
| id | doaj.art-e3a534c68fae4ec3bd5b51f0b0847e18 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-11T09:29:29Z |
| publishDate | 2022-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-e3a534c68fae4ec3bd5b51f0b0847e182022-12-22T04:31:57ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-10-01821011110.1140/epjc/s10052-022-10853-5Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-timesTonatiuh Matos0Omar Gallegos1Pierre-Henri Chavanis2Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPNDepartamento de Física, Centro de Investigación y de Estudios Avanzados del IPNLaboratoire de Physique Théorique, Université de Toulouse, CNRS, UPSAbstract Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.https://doi.org/10.1140/epjc/s10052-022-10853-5 |
| spellingShingle | Tonatiuh Matos Omar Gallegos Pierre-Henri Chavanis Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times European Physical Journal C: Particles and Fields |
| title | Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times |
| title_full | Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times |
| title_fullStr | Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times |
| title_full_unstemmed | Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times |
| title_short | Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times |
| title_sort | hydrodynamic representation and energy balance for dirac and weyl fermions in curved space times |
| url | https://doi.org/10.1140/epjc/s10052-022-10853-5 |
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