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arXiv · 2312.03163

Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle

Jérémie Pierard de Maujouy
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Abstract

We clarify the structure obtained in H\'elein 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.

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Jérémie Pierard de Maujouy. 2023-12-05. Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle. https://doi.org/10.1016/j.geomphys.2024.105297

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