Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle
arXiv:2312.03163 · doi:10.1016/j.geomphys.2024.105297
Abstract
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.
revised and cut down version of arXiv:2201.01108