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arXiv · 2111.12023

Local spin base invariance from a global differential-geometrical point of view

Claudio Emmrich
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Abstract

This article gives a geometric interpretation of the spin base formulation with local spin base invariance of spinors on a curved space-time and in particular of a central element, the global Dirac structure, in terms of principal and vector bundles and their endomorphisms. It is shown that this is intimately related to Spin and Spin^C structures in the sense that the existence of one of those implies the existence of a Dirac structure and allows an extension to local spin base invariance. Vice versa, as a central result, the existence of a Dirac structure implies the existence of a Spin^C structure. Nevertheless, the spin base invariant setting may be considered more general, allowing more physical degrees of freedom. Furthermore, arguments are given that the Dirac structure is a more natural choice as a variable for (quantum) gravity than tetrads/vielbeins.

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Claudio Emmrich. 2021-11-23. Local spin base invariance from a global differential-geometrical point of view. https://doi.org/10.1063/5.0081140

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