Affiliation:
1. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
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 [Formula: see text] structures in the sense that the existence of one of those implies the existence of a Dirac structure and allows for an extension to local spin base invariance. Vice versa, as a central result, the existence of a Dirac structure implies the existence of a [Formula: see text] structure. Nevertheless, the spin base invariant setting may be considered more general, allowing for 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.
Subject
Mathematical Physics,Statistical and Nonlinear Physics