Simultaneous Hamiltonian Treatment of Class A Spacetimes and Reduction of Degrees of Freedom at the Quantum Level

Abstract

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 $C_{\beta \gamma }^{\alpha }$ 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 ansätzen at the quantum level in a way that respects the scalings of the quadratic Hamiltonian constraint.

arXiv commentRevised in 2002, LaTeX, 12 pages, G&C style, published version