Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Nonlinearities in Field Theory, Condensed Matter and
  Analytical Mechanics   There are two very important subjects in physics: Symmetry of dynamical
models and nonlinearity. All really fundamental models are invariant under some
particular symmetry groups. There is also no true physics, no our Universe and
life at all, without nonlinearity. Particularly interesting are essential,
non-perturbative nonlinearities which are not described by correction terms
imposed on some well-defined linear background. Our idea in this paper is that
there exists some mysterious, not yet understood link between essential,
physically relevant nonlinearity and dynamical symmetry, first of all, large
symmetry groups. In some sense the problem is known even in soliton theory,
where the essential nonlinearity is often accompanied by the infinite system of
integrals of motion, thus, by infinite-dimensional symmetry groups. Here we
discuss some more familiar problems from the realm of field theory, condensed
matter physics, and analytical mechanics, where the link between essential
nonlinearity and high symmetry is obvious, even if not yet fully understood.

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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom