Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle
Mathematical Physics
2024-09-02 v1 Differential Geometry
math.MP
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.
Cite
@article{arxiv.2312.03163,
title = {Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle},
author = {Jérémie Pierard de Maujouy},
journal= {arXiv preprint arXiv:2312.03163},
year = {2024}
}
Comments
revised and cut down version of arXiv:2201.01108