Conditional Symmetries and Phase Space Reduction towards G.C.T. Invariant Wave Functions, for the Class A Bianchi Type VI & VII Vacuum Cosmologies

Details Conditional Symmetries and Phase Space Reduction towards G.C.T. Invariant Wave Functions, for the Class A Bianchi Type VI & VII Vacuum Cosmologies Conditional Symmetries and Phase Space Reduction towards G.C.T. Invariant Wave Functions, for the Class A Bianchi Type VI & VII Vacuum Cosmologies

2001-01-26

arxiv.org/abs/gr-qc/0101103v2

Phys.Lett.B514:149-154,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX2e, no figures

Scientific paper

10.1016/S0370-2693(01)00793-6

The quantization of Class A Bianchi Type VI and VII geometries -with all six scale factors, as well as the lapse function and the shift vector present- is considered. A first reduction of the initial 6-dimensional configuration space is 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 revealing a classical integral of motion, tantamount to an extra symmetry of the corresponding classical Hamiltonian. This symmetry generator -member of a larger group- is linear in momenta and corresponds to G.C.T.s through the action of the automorphism group -especially through the action of the outer automorphism subgroup. Thus, a G.C.T. invariant wave function is found, which depends on one combination of the two curvature invariants --which uniquely and irreducibly characterizes the hypersurfaces t=const.

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