Analyticity of Wightman Functions

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Abstract
The problem of mapping certain domains in the space of complex four‐vectors onto the space of their inner products is solved by a novel method. The ``primitive'' domains of regularity of the three and four point Wightman functions are determined. The domains whose X‐space characterization was obtained by Streater, for the holomorphy envelope of the union of several primitive domains (both for the three and four point function) are also determined. The corresponding problem in perturbation theory is examined, and the analytic form of the perturbation theory boundary of the three and four point functions is obtained by the same method. The problem of the four‐point function is reduced to constructing the holomorphy envelope of the union of three domains. It is shown that the boundary of the domain of four‐point singularitites in perturbation theory bears no resemblance to any part of the boundary of the primitive domains, or the domains found or conjectured by Streater.

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