Abstract
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 [1] and the weak spectral condition are equivalent with the Wightman axioms.
Supported by the Russian Foundation of Fundamental Researches under Grant No. 93-011-147.
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References
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© 1995 Springer-Verlag
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Zinoviev, Y.M. (1995). Equivalence of the Euclidean and Wightman field theories. In: Rivasseau, V. (eds) Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics. Lecture Notes in Physics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59190-7_25
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DOI: https://doi.org/10.1007/3-540-59190-7_25
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