The MathaiQuillen formalism and topological field theory
Abstract
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 MathaiQuillen 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 AtiyahJeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over spaces of connections.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 June 1993
 DOI:
 10.1016/03930440(93)90049K
 arXiv:
 arXiv:hepth/9203026
 Bibcode:
 1993JGP....11...95B
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 34 a4.sty pages (Notes of lectures given at the Karpacz Winter School on `Infinite Dimensional Geometry in Physics', 1727 February 1992)