Projective techniques and functional integration for gauge theories

1994/11/17 by Abhay Ashtekar, Jerzy Lewandowski · 12 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Collineation #Cosmology and Gravitation Theories #Discrete mathematics #Euclidean geometry #Gauge theory #General relativity #Geometry #Hausdorff space #Mathematical analysis #Mathematical physics #Mathematics #Modulo #Noncommutative and Quantum Gravity Theories #Projective space #Projective test #Pure mathematics #gr-qc #hep-th

paper · pdf · doi:10.1063/1.531037

published as J.Math.Phys.36:2170-2191,1995 · 36 pages, latex, no figures, Preprint CGPG/94/10-6

arxiv created 1994/11/17 · openalex publication_date 1995/05/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Feynman's path integral
• Representation Theory of Analytic Holonomy C* Algebras

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