The exponential interaction in Rn |
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| Authors: | Sergio Albeverio Giovanni Gallavotti Raphael Høegh Krohn |
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| Institution: | 1. Centre de Physique Théorique, CNRS Marseille, Université d''Aix-Marseille II, UER de Luminy, France;2. Fakultät für Mathematik, Universität Bielefeld, Germany;3. Matematisk Institutt, Universitetet i Oslo, Norway;4. Istituto di Matematica, Università di Roma, Italy |
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| Abstract: | 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. |
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