Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hamiltonian Formulation of Causal Variational Principles   Causal variational principles, which are the analytic core of the physical
theory of causal fermion systems, are found to have an underlying Hamiltonian
structure, giving a formulation of the dynamics in terms of physical fields in
space-time. After generalizing causal variational principles to a class of
lower semi-continuous Lagrangians on a smooth, possibly non-compact manifold,
the corresponding Euler-Lagrange equations are derived. In the first part, it
is shown under additional smoothness assumptions that the space of solutions of
the Euler-Lagrange equations has the structure of a symplectic Fr\'echet
manifold. The symplectic form is constructed as a surface layer integral which
is shown to be invariant under the time evolution. In the second part, the
results and methods are extended to the non-smooth setting. The physical fields
correspond to variations of the universal measure described infinitesimally by
one-jets. Evaluating the Euler-Lagrange equations weakly, we derive linearized
field equations for these jets. In the final part, our constructions and
results are illustrated in a detailed example on $\mathbb{R}^{1,1} \times S^1$
where a local minimizer is given by a measure supported on a two-dimensional
lattice.

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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga