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A stochastic variational condition for the Maxwell connections. (English) Zbl 0960.58018

Using a sort of Malliavin calculus, the author shows that the infinitesimal reduced variation of stochastic parallel displacement on a commutative principal bundle is a martingale if and only if the connection, with respect to which the displacement is produced, satisfies the Maxwell equation.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
60J60 Diffusion processes
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References:

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