Equivalence of the Euclidean and Wightman Field Theories

Details Equivalence of the Euclidean and Wightman Field Theories Equivalence of the Euclidean and Wightman Field Theories

1994-08-02

arxiv.org/abs/hep-th/9408009v1

Commun.Math.Phys. 174 (1995) 1-28

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LATEX, SMI - 94 - 179

Scientific paper

10.1007/3-540-59190-7_25

The new inversion formula for the Laplace transformation of the tempered distributions with supports in the closed positive semiaxis is obtained. The inverse Laplace transform of the tempered distribution is defined by means of the limit of the special distribution constructed from this distribution. The weak spectral condition on the Euclidean Green's functions requires that some of the limits needed for the inversion formula exist for any Euclidean Green's function with even number of variables. We prove that the initial Osterwalder--Schrader axioms (1973) and the weak spectral condition are equivalent with the Wightman axioms.

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