Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional Symmetries, the True Degree of Freedom and G.C.T. Invariant
  Wave functions for the general Bianchi Type II Vacuum Cosmology   The quantization of the most general Bianchi Type II geometry -with all six
scale factors, as well as the lapse function and the shift vector, present- is
considered. In an earlier work, a first reduction of the initial 6-dimensional
configuration space, to a 4-dimensional one, has been achieved by the usage of
the information furnished by the quantum form of the linear constraints.
Further reduction of the space in which the wave function -obeying the
Wheeler-DeWitt equation- lives, is accomplished by unrevealling the extra
symmetries of the Hamiltonian. These symmetries appear in the form of -linear
in momenta- first integrals of motion. Most of these symmetries, correspond to
G.C.T.s through the action of the automorphism group. Thus, a G.C.T. invariant
wave function is found, which depends on the only true degree of freedom, i.e.
the unique curvature invariant, characterizing the hypersurfaces t=const.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg