Interacting relativistic boson fields in the De Sitter universe with two space-time dimensions

The positive temperature Gibbs state of a scalar boson field with a relativistic local self-interaction in two space-time dimensional Minkowski universe is not relativistically invariant. We prove in this paper that the corresponding state in the De Sitter universe is actually relativistically invariant if the temperature is given by T = 1/2 πR where R is the constant radius of curvature of the De Sitter universe. Moreover, the construction shows that the Schwinger functions or imaginary time Wightman functions are the moments of a generalized Markoff process on the sphere of radius R. (orig.)