Brownian pants and Deligne cohomology -: art. no. 033503

We define stochastic pants, and the stochastic parallel transport over them for the Felder-Gawedzki-Kupiainen line bundle over the loop space. It is related to the construction of stochastic integrals, where we cannot use martingale theory in order to define them. We get a stochastic fusion of the two line bundles when the two loops meet. (C) 2005 American Institute of Physics.