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Projective Techniques and Functional Integration

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arxiv gr-qc/9411046 v1 pith:XOKQCMH6 submitted 1994-11-17 gr-qc hep-th

Abhay Ashtekar , Jerzy Lewandowski This is my paper · ORCID
classification gr-qchep-th
keywords integrationprojectivefunctionalspacesapproachdimensionalgaugegeneral
verification ladder T0 review T1 audit T2 compute T3 formal

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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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Cited by 5 Pith papers

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