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Ashtekar, Abhay; Lewandowski, Jerzy

Projective techniques and functional integration for gauge theories. (English) Zbl 0844.58009

J. Math. Phys. 36, No. 5, 2170-2191 (1995).
Summary: 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 nonlinear, 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.

Cited in 1 Review
Cited in 83 Documents

MSC:

58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
83C47 Methods of quantum field theory in general relativity and gravitational theory
81T13 Yang-Mills and other gauge theories in quantum field theory

Keywords:

integration; infinite dimensional spaces; projective limits; gauge theories; quantum general relativity
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\textit{A. Ashtekar} and \textit{J. Lewandowski}, J. Math. Phys. 36, No. 5, 2170--2191 (1995; Zbl 0844.58009)
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References:

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[2] DOI: 10.1007/BF00761713 · Zbl 0798.58009
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