Equivalence of Euclidean and Wightman field theories
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A new inversion formula for the Laplace transformation of tempered distributions with supports in the closed positive semiaxis is obtained. The inverse Laplace transform of a tempered distribution is defined by means of a limit of a special distribution constructed from this distribution. The weak spectral condition on the Euclidean Green's functions implies that some of the limits needed for the inversion formula exist for any Euclidean Green's function with an even number of variables. We then prove that the initial Osterwalder-Schrader axioms  and the weak spectral condition are equivalent with the Wightman axioms.
KeywordsNeural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics
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