Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of Lagrangian First-order Classical Field Theories   We construct a lagrangian geometric formulation for first-order field
theories using the canonical structures of first-order jet bundles, which are
taken as the phase spaces of the systems in consideration. First of all, we
construct all the geometric structures associated with a first-order jet bundle
and, using them, we develop the lagrangian formalism, defining the canonical
forms associated with a lagrangian density and the density of lagrangian
energy, obtaining the {\sl Euler-Lagrange equations} in two equivalent ways: as
the result of a variational problem and developing the {\sl jet field
formalism} (which is a formulation more similar to the case of mechanical
systems). A statement and proof of Noether's theorem is also given, using the
latter formalism. Finally, some classical examples are briefly studied.

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The categories of this paper are: nlin
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat