Conditional symmetries and the quantization of Bianchi Type I vacuum cosmologies with and without cosmological constant

摘要: In this paper, the quantization of most general Bianchi Type I geometry, with and without a cosmological constant, is considered. spirit identifying subsequently removing as many gauge degrees freedom possible, reduction initial six-dimensional configuration space presented. This achieved by imposing additional conditions on wavefunction, quantum version the, linear in momenta, classical integrals motion (conditional symmetries). The vector fields inferred from these induce, through their integral curves, motions which can be identified to action automorphism group I, i.e. GL(3,). Thus, wavefunction depending one degree freedom, namely determinant scale factor matrix, found. A measure for constructing Hilbert proposed. respects above-mentioned symmetries also invariant under property covariance arbitrary scalings Hamiltonian (quadratic constraint).