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arXiv · gr-qc/9411046

Projective Techniques and Functional Integration

Abhay Ashtekar·Jerzy Lewandowski
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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.)

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BibTeXRIS

Abhay Ashtekar, Jerzy Lewandowski. 1994-11-17. Projective Techniques and Functional Integration. https://doi.org/10.1063/1.531037

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