FIELD OF SINE-GORDON TYPE IN SPACETIME OF ARBITRARY DIMENSION - EXISTENCE OF THE NELSON MEASURE

A model of a field with bounded current density is investigated. It is shown that there exists an infinite-fold integral that determines a g enerating functional of the Schwinger functions. It is shown that this functional is the Fourier transform of a probability measure on the f ield trajectories that is concentrated in a Hilbert subspace of the sp ace of tempered distributions of first order of singularity. It is sho wn that the field satisfies the strong regularity axiom of Osterwalder and Schrader.