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 as constructed in 1] is not relativistic invariant. We prove in this paper that the corresponding state in the De Sitter universe is actually relativistic invariant if the temperature is given byT=1/2πR whereR is the constant radius of curvature of the De Sitter universe. Moreover the construction gives that the Schwinger functions or imaginary time Wightman functions are the moments of a generalized Markoff process on the sphere of radiusR.