Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Causal Variational Principles in the $\sigma$-Locally Compact Setting:
  Existence of Minimizers   We prove the existence of minimizers of causal variational principles on
second countable, locally compact Hausdorff spaces. Moreover, the corresponding
Euler-Lagrange equations are derived. The method is to first prove the
existence of minimizers of the causal variational principle restricted to
compact subsets for a lower semi-continuous Lagrangian. Exhausting the
underlying topological space by compact subsets and rescaling the corresponding
minimizers, we obtain a sequence which converges vaguely to a regular Borel
measure of possibly infinite total volume. It is shown that, for continuous
Lagrangians of compact range, this measure solves the Euler-Lagrange equations.
Furthermore, we prove that the constructed measure is a minimizer under
variations of compact support. Under additional assumptions, it is proven that
this measure is a minimizer under variations of finite volume. We finally
extend our results to continuous Lagrangians decaying in entropy.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat