Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Presymplectic structures and intrinsic Lagrangians for massive fields   We study the construction of the so-called intrinsic action for PDEs equipped
with compatible presymplectic structures. In particular, we explicitly
demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity
is the familiar first-order Palatini action. Our main focus in this work is the
massive spin-2 field, where the natural presymplectic structure is not complete
in the sense that the associated intrinsic action does not reproduce all the
equations of motion. We explicitly relate this feature to the differential
consequences of the zeroth order in the genuine Lagrangian formulation of Fierz
and Pauli. Moreover, a minimal multisymplectic extension of the intrinsic
action that produces all the equations of motion is constructed and it is
argued that systems of this type can be naturally regarded as multidimensional
analogs of mechanical systems with constraints. Finally, we extend the
considerations to the massive spin-3 field and argue that the extension to all
the massive higher spins should be straightforward as well.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom