Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries and physical functions in general gauge theory   The aim of the present article is to describe the symmetry structure of a
general gauge (singular) theory, and, in particular, to relate the structure of
gauge transformations with the constraint structure of a theory in the
Hamiltonian formulation. We demonstrate that the symmetry structure of a theory
action can be completely revealed by solving the so-called symmetry equation.
We develop a corresponding constructive procedure of solving the symmetry
equation with the help of a special orthogonal basis for the constraints. Thus,
we succeed in describing all the gauge transformations of a given action. We
find the gauge charge as a decomposition in the orthogonal constraint basis.
Thus, we establish a relation between the constraint structure of a theory and
the structure of its gauge transformations. In particular, we demonstrate that,
in the general case, the gauge charge cannot be constructed with the help of
some complete set of first-class constraints alone, because the charge
decomposition also contains second-class constraints. The above-mentioned
procedure of solving the symmetry equation allows us to describe the structure
of an arbitrary symmetry for a general singular action. Finally, using the
revealed structure of an arbitrary gauge symmetry, we give a rigorous proof of
the equivalence of two definitions of physicality condition in gauge theories:
one of them states that physical functions are gauge-invariant on the
extremals, and the other requires that physical functions commute with FCC (the
Dirac conjecture).

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol