Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivector Field Formulation of Hamiltonian Field Theories: Equations
  and Symmetries   We state the intrinsic form of the Hamiltonian equations of first-order
Classical Field theories in three equivalent geometrical ways: using
multivector fields, jet fields and connections. Thus, these equations are given
in a form similar to that in which the Hamiltonian equations of mechanics are
usually given. Then, using multivector fields, we study several aspects of
these equations, such as the existence and non-uniqueness of solutions, and the
integrability problem. In particular, these problems are analyzed for the case
of Hamiltonian systems defined in a submanifold of the multimomentum bundle.
Furthermore, the existence of first integrals of these Hamiltonian equations is
considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl
general symmetries} of the system is discussed. Noether's theorem is also
stated in this context, both the ``classical'' version and its generalization
to include higher-order Cartan-Noether symmetries. Finally, the equivalence
between the Lagrangian and Hamiltonian formalisms is also discussed.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg