Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert space built over connections with a non-compact structure group   Quantization of general relativity in terms of SL(2,C)-connections (i.e. in
terms of the complex Ashtekar variables) is technically difficult because of
the non-compactness of SL(2,C). The difficulties concern the construction of a
diffeomorphism invariant Hilbert space structure on the space of cylindrical
functions of the connections. We present here a 'toy' model of such a Hilbert
space built over connections whose structure group is the group of real
numbers. We show that in the case of any Hilbert space built analogously over
connections with any non-compact structure group (this includes some models
presented in the literature) there exists an obstacle which does not allow to
define a *-representation of cylindrical functions on the Hilbert space by the
multiplication map which is the only known way to define a diffeomorphism
invariant representation of the functions.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th