TOPOLOGICAL MEASURE AND GRAPH-DIFFERENTIAL GEOMETRY ON THE QUOTIENT SPACE OF CONNECTIONS

JERZY LEWANDOWSKI
1994 International Journal of Modern Physics D  
(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
more » ... trip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly, to become essentially self adjoint operators.
doi:10.1142/s0218271894000307 fatcat:nv7ahruhajgypg2ewsyfbxc5ae