The Mathai-Quillen Formalism and Topological Field Theory

Details The Mathai-Quillen Formalism and Topological Field Theory The Mathai-Quillen Formalism and Topological Field Theory

1992-03-10

arxiv.org/abs/hep-th/9203026v1

J.Geom.Phys. 11 (1993) 95-127

Physics

High Energy Physics

High Energy Physics - Theory

34 a4.sty pages (Notes of lectures given at the Karpacz Winter School on `Infinite Dimensional Geometry in Physics', 17-27 Feb

Scientific paper

10.1016/0393-0440(93)90049-K

These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of the Mathai-Quillen formalism for finite dimensional vector bundles; the definition of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over spaces of connections.

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