Banach manifold structure and infinite-dimensional analysis for causal fermion systems

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 Fréchet-smooth Riemannian metric. The so-called expedient differential calculus...

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Vydáno v:Annals of global analysis and geometry Ročník 60; číslo 2; s. 313 - 354
Hlavní autoři: Finster, Felix, Lottner, Magdalena
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.09.2021
Springer Nature B.V
Témata:
Analysis
Banach spaces
Continuity (mathematics)
Differential calculus
Differential Geometry
Dimensional analysis
Fermions
Geometry
Global Analysis and Analysis on Manifolds
Manifolds (mathematics)
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Subspaces
Infinite-dimensional analysis
Banach manifolds
Non-smooth analysis
Expedient differential calculus
Causal fermion systems
Fréchet-smooth Riemannian structures
ISSN:0232-704X, 1572-9060
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Popis
Shrnutí: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 Fréchet-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 Hölder continuous functions which are differentiable on expedient subspaces. These results are made applicable to causal fermion systems by proving that the causal Lagrangian is Hölder continuous. Moreover, Hölder continuity is analyzed for the integrated causal Lagrangian.
Bibliografie:ObjectType-Article-1
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ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-021-09775-4