EXPONENTIAL INTERACTION IN RN

We prove that the Schwinger functions for the ultraviolet cut-off exponential interaction with euclidean measure exp {;-λ∫Λ:eαξk(x):dx} dμ0(ξ/ ∫ exp{-λ∫Λ:eαξk(x):dx} dμ0(ξ), λ > 0, converge as the ultraviolet cut-off is removed. The limits are the free Schwinger functions in the case of space-time dimension n ≥ 3. In the case n = 2 this holds for |α| sufficiently big, whereas for |α| < 2 √π, one has the well-known nontrivial Schwinger functions of the exponential interaction. © 1979.