Euclidean Reconstruction in Quantum Field Theory: Between tempered distributions and Fourier Hyperfunctions

Details Euclidean Reconstruction in Quantum Field Theory: Between tempered distributions and Fourier Hyperfunctions Euclidean Reconstruction in Quantum Field Theory: Between tempered distributions and Fourier Hyperfunctions

1998-11-02

arxiv.org/abs/math-ph/9811002v1

Physics

Mathematical Physics

20 pages, 5 figures, AMSTeX with PICTeX macros, Talk given at the second Frankfurt-Krakow Operator Theory Seminar, April 1997

Scientific paper

I want to point out the mathematical difficulties that arise in the study of the relation of Wightman and Euclidean quantum field theory, i.e., the relation between the hierarchies of Wightman and Schwinger functions. The two extreme cases where the reconstructed Wightman functions are either tempered distributions - the well-known Osterwalder-Schrader reconstruction - or modified Fourier hyperfunctions are discussed in some detail. Finally, some perpectives towards a classification of Euclidean reconstruction theorems are outlined and preliminary steps in that direction are presented.

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