Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Historical Hamiltonian Dynamics: symplectic and covariant   This paper presents a "historical" formalism for dynamical systems, in its
Hamiltonian version (Lagrangian version was presented in a previous paper). It
is universal, in the sense that it applies equally well to time dynamics and to
field theories on space-time. It is based on the notion of (Hamiltonian)
histories, which are sections of the (extended) phase space bundle. It is
developed in the space of sections, in contradistinction with the usual
formalism which works in the bundle manifold. In field theories, the formalism
remains covariant and does not require a spitting of space-time. It considers
space-time exactly in the same manner than time in usual dynamics, both being
particular cases of the evolution domain. It applies without modification when
the histories (the fields) are forms rather than scalar functions, like in
electromagnetism or in tetrad general relativity. We develop a differential
calculus in the infinite dimensional space of histories. It admits a
(generalized) symplectic form which does not break the covariance. We develop a
covariant symplectic formalism, with generalizations of usual notions like
current conservation, Hamiltonian vector-fields, evolution vector-field,
brackets, ... The usual multisymplectic approach derives form it, as well as
the symplectic form introduced by Crnkovic and Witten in the space of
solutions.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg