Finster, Felix and Kindermann, Sebastian (2020) A gauge fixing procedure for causal fermion systems. JOURNAL OF MATHEMATICAL PHYSICS, 61 (8): 082301. ISSN 0022-2488, 1089-7658
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Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper, it is explained and worked out in detail that, despite this local gauge freedom, the structures of a causal fermion system give rise to distinguished gauges where the local gauge freedom is fixed completely up to global gauge transformations. The main method is to use spectral and polar decompositions of operators on Hilbert spaces and on indefinite inner product spaces. We also introduce and make use of a Riemannian metric, which is induced on the manifold of all regular correlation operators by the Hilbert-Schmidt scalar product. Gaussian coordinate systems corresponding to this Riemannian metric are constructed. Moreover, we work with so-called wave charts where the physical wave functions are used as coordinates. Our constructions and results are illustrated in the example of Dirac sea configurations in finite and infinite spatial volume.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LIGHT-CONE EXPANSION; DIRAC SEA; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Mar 2021 10:13 |
| Last Modified: | 17 Mar 2021 10:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44102 |
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