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Characterizing Yang–Mills Fields by Stochastic Parallel Transport

✍ Scribed by Robert Otto Bauer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
278 KB
Volume
155
Category
Article
ISSN
0022-1236

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✦ Synopsis

We give a new stochastic approach to Yang Mills fields on vector bundles by studying the derivative of the stochastic parallel transport in the vector bundle under a variation of connection. We establish martingale criterions for variations transversal to the gauge orbit and for Yang Mills fields using variations induced by the flow of vector fields of gradient type on the base manifold. In dimension four we link the local Yang Mills action to the quadratic variation of the derivative process defined by scalings of the driving Brownian motion in a coordinate chart.

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