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.


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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