A Universal Spinor Bundle and the Einstein-Dirac-Maxwell Equation as a Variational Theory
arXiv:1504.01034 · doi:10.1007/s11005-016-0929-4
Abstract
Not only the Dirac operator, but also the spinor bundle of a pseudo-Riemannian manifold depends on the underlying metric. This leads to technical difficulties in the study of problems where many metrics are involved, for instance in variational theory. We construct a natural finite dimensional bundle, from which all the metric spinor bundles can be recovered including their extra structure. In the Lorentzian case, we also give some applications to Einstein-Dirac-Maxwell theory as a variational theory and show how to coherently define a maximal Cauchy development for this theory.
20 pages, presentation simplified, result about universal Dirac-operator added