Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-07-13
Commun.Math.Phys.226:377-391,2002
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, LaTeX2e, no figures, one table, to appear in Communications in Mathematical Physics
Scientific paper
10.1007/s002200200611
An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are the --up to 3-- curvature invariants. An apparent discrepancy between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class A Bianchi Types, occurs due to the existence of the Outer Automorphism Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum version of some classical integrals of motion (conditional symmetries) which are recognized as corresponding to the Outer Automorphisms.
Christodoulakis Th.
Korfiatis E.
Papadopoulos G. O.
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