Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-09-21
Phys.Lett.B501:264-268,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
10 pages, no figures, LaTeX2e Typesetting system
Scientific paper
10.1016/S0370-2693(01)00119-8
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.
Christodoulakis Th.
Papadopoulos G. O.
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