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

Robert Otto Bauer

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number1
    StatePublished - Feb 2003

    ASJC Scopus subject areas

    • Analysis


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