SIMULTANEOUS HAMILTONIAN TREATMENT OF CLASS A SPACETIMES AND REDUCTION OF DEGREES OF FREEDOM AT THE QUANTUM LEVEL
2002
We consider the quantization of a general spatially homogeneous space-time belonging to an arbitrary but fixed Class A Bianchi type. Exploiting the information furnished by the quantum version of the momentum constraints, we use as variables the two simplest contractions of $C^{\alpha}_{\beta \gamma}$ and $\gamma_{\alpha \beta}$ as well as the determinant of $\gamma_{\alpha \beta}$ ; We thus arrive at an equation for the wave function in terms of these quantities. This fact enables us to treat in a uniform manner all Class A cosmologies. For these spacetimes the Langrangian used correctly reproduces Einstein's equations. We also discuss the imposition of simplifying ans\"{a}tzen at the quantum level in a way that respects the scalings of the quadratic Hamiltonian constraint.
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