Finster, Felix and Oppio, Marco (2020) Local algebras for causal fermion systems in Minkowski space. JOURNAL OF MATHEMATICAL PHYSICS, 61 (11): 112303. ISSN 0022-2488, 1089-7658
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A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the differences to the canonical commutation relations are discussed. It is shown that the spacetime point operators associated with a Cauchy surface satisfy a time slice axiom. It is proven that the algebra generated by operators in an open set is irreducible as a consequence of Hegerfeldt's theorem. The light-cone structure is recovered by analyzing the expectation values of the operators in the algebra in the limit when the regularization is removed. It is shown that every spacetime point operator commutes with the algebras localized away from its null cone, up to small corrections involving the regularization length.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Mar 2021 09:55 |
| Last Modified: | 08 Mar 2021 09:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43462 |
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