Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections

Details Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections

1994-06-16

arxiv.org/abs/gr-qc/9406025v1

Int.J.Mod.Phys.D3:207-210,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pp., Proceedings of ``Journees Relativistes 1993''

Scientific paper

10.1142/S0218271894000307

(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of the quotient space. The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly, to become essentially self adjoint operators.

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