Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929478922403840 |
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| author | de Maujouy, Jérémie Pierard |
| author_facet | de Maujouy, Jérémie Pierard |
| contents | We clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained structure is locally equivalent to a frame bundle which we term "generalised frame bundle". In the same time, we enrich the model with a Dirac spinor coupled to the Einstein-Cartan spacetime. The obtained variational equations generalise the usual Einstein-Cartan-Dirac field equations in that they are shown to imply the usualy field equations when the generalised frame bundle is a standard frame bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle de Maujouy, Jérémie Pierard Mathematical Physics Differential Geometry We clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained structure is locally equivalent to a frame bundle which we term "generalised frame bundle". In the same time, we enrich the model with a Dirac spinor coupled to the Einstein-Cartan spacetime. The obtained variational equations generalise the usual Einstein-Cartan-Dirac field equations in that they are shown to imply the usualy field equations when the generalised frame bundle is a standard frame bundle. |
| title | Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle |
| topic | Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2312.03163 |