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Yang-Mills fields and stochastic parallel transport in small geodesic balls

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  • Bauer, Robert Otto

Abstract

We develop a new method to obtain stochastic characterizations of Yang-Mills fields. Our main tool is the Itô-equation for the stochastic parallel transport. We estimate the drift terms in a small ball of radius [var epsilon] and find that for a general connection the average rotation is of order [var epsilon]3 but that for a Yang-Mills connections the average rotation is of order [var epsilon]4. Using a Doob h-transform we give a new proof of the stochastic characterization of Yang-Mills fields by S. Stafford. Varying the starting point of the Brownian motion we obtain an unconditioned version of this result. By considering the horizontal Laplace equation we then apply our result to obtain a new analytic characterization of Yang-Mills fields.

Suggested Citation

  • Bauer, Robert Otto, 2000. "Yang-Mills fields and stochastic parallel transport in small geodesic balls," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 213-226, October.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:2:p:213-226
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