Projective techniques and functional integration for gauge theories

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.

Original languageEnglish (US)
Pages (from-to)2170-2191
Number of pages22
JournalJournal of Mathematical Physics
Volume36
Issue number5
DOIs
StatePublished - Jan 1 1995

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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