量子场论中的欧几里德重建：在回火分布和傅立叶超函数之间
Euclidean Reconstruction in Quantum Field Theory: Between tempered distributions and Fourier Hyperfunctions
摘要：
我想指出在研究怀特曼和欧几里德量子场论的关系时出现的数学困难，即，Wightman函数和Schwinger函数的关系。两个极端的情况下，重建的Wightman函数是回火分布-著名的Osterwalder-Schrader重建-或修改后的傅立叶超函数进行了详细讨论。最后，一些观点对分类的欧几里得重建定理的概述，并在该方向的初步步骤。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
