Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert space cocycles as representations of $(3+1)-$ D current algebras   It is proposed that instead of normal representations one should look at
cocycles of group extensions valued in certain groups of unitary operators
acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing
with groups associated to current algebras in gauge theories in $3+1$
space-time dimensions. The appropriate cocycle is evaluated in the case of the
group of smooth maps from the physical three-space to a compact Lie group. The
cocyclic representation of a component $X$ of the current is obtained through
two regularizations, 1) a conjugation by a background potential dependent
unitary operator $h_A,$ 2) by a subtraction $-h_A^{-1}\Cal L_X h_A,$ where
$\Cal L_X$ is a derivative along a gauge orbit. It is only the total operator
$h_A^{-1} Xh_A-h_A^{-1}\Cal L_X h_A$ which is quantizable in the Fock space
using the usual normal ordering subtraction.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn