We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.
Contents1 Introduction 83 2. Test Functions and Distributions 85 3. The Axioms, Main Theorems 87 4. TheoremE->R 90 4.1. Construction of the Wightman Distributions 90 4.
We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.
Table of ContentsI. Introduction 281 II. Notations 283 III. The Equivalence Theorem Revisited 285 IV. The Main Result: Another Reconstruction Theorem 287 IV. 1 Linear Growth Condition and Statement of Results 287 IV.2 Proof of Theorem £'->#' 288 V. The Analytic Continuation . 289 V.I Real Analyticity 291 V.2 Towards the Real World 293 VI. The Temperedness Estimate 297 VI.1 From Distributions to Functions 297 VI.2 Continuing the Estimates 301 VII. Appendix 303 References 305 * Supported in part by the National Science Foundation under Grant MPS73-05037 A01. Alfred P. Sloan Foundation Fellow. 1 For verification of this assertion the reader should consult the 1973 Erice Lectures on Constructive Quantum Field Theory [19], where also references and historical accounts can be found.
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