### 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 language | English (US) |
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Pages (from-to) | 2170-2191 |

Number of pages | 22 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*36*(5), 2170-2191. https://doi.org/10.1063/1.531037