Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear $\Sigma$ Model in the Gaussian Functional Approximation   We apply a self-consistent relativistic mean-field variational ``Gaussian
functional'' (or Hartree) approximation to the linear $\sigma$ model with
spontaneously and explicitly broken chiral O(4) symmetry. We set up the
self-consistency, or ``gap'' and the Bethe-Salpeter equations. We check and
confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone
theorem and the (partial) axial current conservation [CAC], both in and away
from the chiral limit. With explicit chiral symmetry breaking we confirm the
Dashen relation for the pion mass and partial CAC. We solve numerically the gap
and Bethe-Salpeter equations, discuss the solutions' properties and the
particle content of the theory.

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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex