Random Holonomy for Yang-Mills Fields: Long-Time Asymptotics

Robert Otto Bauer

Research output: Contribution to journalArticlepeer-review

Abstract

We study weak and strong convergence of the stochastic parallel transport for time → ∞ on Euclidean space. We show that the asymptotic behavior can be controlled by the Yang-Mills action and the Yang-Mills equations. For open paths we show that under appropriate curvature conditions there exits a gauge in which the stochastic parallel transport converges almost surely. For closed paths we show that there exists a gauge invariant notion of a weak limit of the random holonomy and we give conditions that insure the existence of such a limit. Finally, we study the asymptotic behavior of the average of the random holonomy in the case of t'Hooft's 1-instanton.

Original languageEnglish (US)
Pages (from-to)43-57
Number of pages15
JournalPotential Analysis
Volume18
Issue number1
DOIs
StatePublished - Feb 2003

ASJC Scopus subject areas

  • Analysis

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