Abstract
The unnormalized doubly cutoff Schwinger functions converge as the ultraviolet cutoff is removed. The limits, the finite volume unnormalized Schwinger functions, are tempered distributions and areC ∞ in the coupling constant. They have asymptotic expansions given by perturbation theory. For λ sufficiently small they can be normalized and then they are the moments of a measure onI′ ℝ (IR3).
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References
Fröhlich, J.: Schwinger functions and their generating functionals (preprint)
Glimm, J.: Commun. math. Phys.10, 1 (1968)
Glimm, J., Jaffe, A.: Fortsch. Physik21, 327 (1973)
Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in theP(ϕ)2 quantum field model (preprint)
Glimm, J., Jaffe, A., Spencer, T.: The particle structure of the weakly coupledP(ϕ)2 model and other applications of high temperature expansions. In: Velo, G., Wightman, A.S. (Eds.): Constructive quantum field theory, 1973. Erice Lectures, Vol. 25, Berlin-Heidelberg-New York: Springer 1973
Symanzik, K.: A modified model of Euclidean quantum field theory. C.I.M.S. Report IMM-NYU 327, June 1964
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Communicated by A. S. Wightman
Supported in part by the National Science Foundation under Grant GP 40354X.
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Feldman, J. The λϕ 43 field theory in a finite volume. Commun.Math. Phys. 37, 93–120 (1974). https://doi.org/10.1007/BF01646205
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DOI: https://doi.org/10.1007/BF01646205