On \(Y M_ 2\) measures and area-preserving diffeomorphisms
type: Item
instance of: scholarly article
title: On \(Y M_ 2\) measures and area-preserving diffeomorphisms
zbMATH Open document ID: 0866.58017
DOI: 10.1016/0393-0440(95)00034-8
author: Doug Pickrell
published in: Journal of Geometry and Physics
publication date: 1997-07-30T00:00:00Z
review text: It is known that for a given gauge group and compact Riemannian two-manifold, the associated Yang-Mills measure can be defined directly as a finitely additive measure on the space of connections, and this finitely additive measure is invariant with respect to \textit{SDiff}, the group of all area-preserving diffeomorphisms of the surface. The first objective of this work is to study whether this symmetry essentially characterizes the projection of the Yang-Mills measure to the space of gauge equivalence classes. This study needs the construction of an \textit{SDiff}-equivariant completion of the space of continuous connections, such that the projection of the Yang-Mills measure to the space of gauge equivalence classes has a countably additive extension. The coupling of the Yang-Mills measure to determinants of Dirac operators is also considered. The basic problems are to prove that the coupled measure is absolutely continuous with respect to the background Yang-Mills measure, to find a reasonable formula for the Radon-Nikodym derivative, and to analyse the action of \textit{SDiff}.
Mathematics Subject Classification ID: 58D20
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 53C07
zbMATH DE Number: 927899
zbMATH Keywords: area-preserving diffeomorphisms
zbMATH Keywords: Yang-Mills measure
zbMATH Keywords: determinants of Dirac operators
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00034-8
OpenAlex ID: W2006324080
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description: scientific article; zbMATH DE number 927899