1992/03/10 by Matthias Blau, M. Blau · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Bundle #Combinatorics #Fiber bundle #Formalism (music) #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum field theory #Theoretical physics #Topological quantum field theory #Topology (electrical circuits) #Vector bundle #hep-th #math.QA
paper · pdf · doi:10.1016/0393-0440(93)90049-k
published as J.Geom.Phys. 11 (1993) 95-127 · 34 a4.sty pages (Notes of lectures given at the Karpacz Winter School on `Infinite Dimensional Geometry in Physics', 17-27 February 1992)
arxiv created 1992/03/10 · openalex publication_date 1993/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.