Markov cosurfaces and gauge fields

The authors give a general construction of homogeneous Markov fields associated with d-1 hypersurfaces on a d-dimensional Riemannian manifold with values in a Lie group G. In the case d = 2 these 'Markov cosurfaces' coincide with pure continuum gauge fields with values in G. The constructed Markov cosurfaces have properties of the type of those postulated for Wilson loops Schwinger functions in the case of gauge fields and lead to relativistic quantum fields. The Markov cosurfaces provide an extension of Markov processes for the case where time points are replaced by d-1-dimensional hypersurfaces, and a corresponding extension of stochastic differential equations if given. The Markov cosurfaces are also shown to be obtainable from lattice models. (Auth.)