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

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.


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
Full Text: DOI arXiv


[1] DOI: 10.1088/0264-9381/9/6/004 · Zbl 0773.53033
[2] DOI: 10.1007/BF00761713 · Zbl 0798.58009
[3] DOI: 10.1016/0550-3213(89)90278-2
[4] DOI: 10.1016/0550-3213(89)90278-2
[5] DOI: 10.1007/BF01221253 · Zbl 0629.58037
[6] DOI: 10.1103/PhysRevD.24.2160
[7] DOI: 10.1088/0264-9381/10/5/008 · Zbl 0808.53027
[8] DOI: 10.1007/BF01646034 · Zbl 0287.28006
[9] DOI: 10.1007/BF01646034 · Zbl 0287.28006
[10] DOI: 10.1016/0370-1573(79)90083-8
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