Abhay Ashtekar, Jerzy Lewandowski
Projective Techniques and Functional Integration for Gauge Theories
The paper is published: J. Math. Phys. 36, 5 (1995) 2170-2191

MSC:

58B20 Riemannian, Finsler and other geometric structures, See also {53C20, 53C60}

83C47 Quantum field theory aspects, See also {81T20}

81T13 Yang-Mills and other gauge theories, See also {53C07,

Abstract: A general framework for integration over certain infinite dimensional
spaces is first developed using projective limits of a projective
family of compact Hausdorff spaces. The procedure is then applied to
gauge theories to carry out integration over the non-linear, infinite
dimensional spaces of connections modulo gauge transformations. This
method of evaluating functional integrals can be used either in the
Euclidean path integral approach or the Lorentzian canonical approach.
A number of measures discussed are diffeomorphism invariant and
therefore of interest to (the connection dynamics version of) quantum
general relativity. The account is pedagogical; in particular prior
knowledge of projective techniques is not assumed.

Keywords: integration, infinite dimensional spaces, projective limits, gauge theories, quantum general relativity