Fundamental geometric structures for the Dirac equation in general relativity. (English) Zbl 0986.83027
Summary: We present an axiomatic approach to Dirac s equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.
MSC:
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 15A66 | Clifford algebras, spinors |
| 53B35 | Local differential geometry of Hermitian and Kählerian structures |
