Finster, Felix and Lottner, Magdalena (2021) Banach manifold structure and infinite-dimensional analysis for causal fermion systems. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 60 (2). pp. 313-354. ISSN 0232-704X, 1572-9060
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A mathematical framework is developed for the analysis of causal fermion systems in the infinite-dimensional setting. It is shown that the regular spacetime point operators form a Banach manifold endowed with a canonical Frechet-smooth Riemannian metric. The so-called expedient differential calculus is introduced with the purpose of treating derivatives of functions on Banach spaces which are differentiable only in certain directions. A chain rule is proven for Holder continuous functions which are differentiable on expedient subspaces. These results are made applicable to causal fermion systems by proving that the causal Lagrangian is Holder continuous. Moreover, Holder continuity is analyzed for the integrated causal Lagrangian.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Banach manifolds; Causal fermion systems; Infinite-dimensional analysis; Expedient differential calculus; Frechet-smooth Riemannian structures; Non-smooth analysis |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Jul 2022 06:30 |
| Last Modified: | 06 Jul 2022 06:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45743 |
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