Projective Techniques and Functional Integration
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. (For the special JMP issue on Functional Integration, edited by C. DeWitt-Morette.)
Cite
@article{arxiv.gr-qc/9411046,
title = {Projective Techniques and Functional Integration},
author = {Abhay Ashtekar and Jerzy Lewandowski},
journal= {arXiv preprint arXiv:gr-qc/9411046},
year = {2010}
}
Comments
36 pages, latex, no figures, Preprint CGPG/94/10-6