Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On covariant phase space methods   It is well known that the Lagrangian and the Hamiltonian formalisms can be
combined and lead to "covariant symplectic" methods. For that purpose a
"pre-symplectic form" has been constructed from the Lagrangian using the
so-called Noether form. However, analogously to the standard Noether currents,
this symplectic form is only determined up to total divergences which are
however essential ingredients in gauge theories.
  We propose a new definition of the symplectic form which is covariant and
free of ambiguities in a general first order formulation. Indeed, our
construction depends on the equations of motion but not on the Lagrangian. We
then define a generalized Hamiltonian which generates the equations of motions
in a covariant way. Applications to Yang-Mills, general relativity,
Chern-Simons and supergravity theories are given. We also consider nice sets of
possible boundary conditions that imply the closure and conservation of the
total symplectic form.
  We finally revisit the construction of conserved charges associated with
gauge symmetries, from both the "covariant symplectic" and the "covariantized
Regge-Teitelboim" points of view. We find that both constructions coincide when
the ambiguity in the Noetherian pre-symplectic form is fixed using our new
prescription. We also present a condition of integrability of the equations
that lead to these quantities.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg