Abstract
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.
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Communicated by A. S. Wightman
Supported in part by the Italian Ministry of Education.
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Figari, R., Höegh-Krohn, R. & Nappi, C.R. Interacting relativistic boson fields in the De Sitter universe with two space-time dimensions. Commun.Math. Phys. 44, 265–278 (1975). https://doi.org/10.1007/BF01609830
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DOI: https://doi.org/10.1007/BF01609830