On Y M2 measures and area-preserving diffeomorphisms

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For a given gauge group and compact Riemannian two-manifold, it is known that 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 SDiff, the group of all area-preserving diffeomorphisms of the surface. The first question we address is whether this symmetry essentially characterizes the projection of the Yang-Mills measure to the space of gauge equivalence classes. The proper formulation of this question entails the construction of an 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. We also consider the coupling of the Yang-Mills measure to determinants of Dirac operators. 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 analyze the action of SDiff.

Original languageEnglish (US)
Pages (from-to)315-367
Number of pages53
JournalJournal of Geometry and Physics
Volume19
Issue number4
DOIs
StatePublished - Aug 1996

Fingerprint

Diffeomorphisms
Yang-Mills
preserving
Finitely Additive Measure
Equivalence class
Gauge
Projection
Radon-Nikodym Derivative
equivalence
projection
Gauge Group
Dirac Operator
Absolutely Continuous
Equivariant
Completion
Determinant
radon
determinants
Symmetry
Invariant

Keywords

  • Sdiff
  • Wiener measures
  • Yang-mills measures
  • Zeta determinants

ASJC Scopus subject areas

  • Geometry and Topology
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

On Y M2 measures and area-preserving diffeomorphisms. / Pickrell, Douglas M.

In: Journal of Geometry and Physics, Vol. 19, No. 4, 08.1996, p. 315-367.

Research output: Contribution to journalArticle

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