Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
Fr\'echet-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 H\"older continuous functions which are differentiable on
expedient subspaces. These results are made applicable to causal fermion
systems by proving that the causal Lagrangian is H\"older continuous. Moreover,
H\"older continuity is analyzed for the integrated causal Lagrangian.

12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th