Yang–Mills elds and stochastic parallel transport in small geodesic balls(
نویسنده
چکیده
We develop a new method to obtain stochastic characterizations of Yang–Mills elds. Our main tool is the Itô-equation for the stochastic parallel transport. We estimate the drift terms in a small ball of radius and nd that for a general connection the average rotation is of order 3 but that for a Yang–Mills connections the average rotation is of order . Using a Doob h-transform we give a new proof of the stochastic characterization of Yang–Mills elds by S. Sta ord. 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 elds. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 58G32; 60H30
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