Projective Techniques and Functional Integration

Details Projective Techniques and Functional Integration Projective Techniques and Functional Integration

1994-11-17

arxiv.org/abs/gr-qc/9411046v1

J.Math.Phys.36:2170-2191,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages, latex, no figures, Preprint CGPG/94/10-6

Scientific paper

10.1063/1.531037

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.)

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