全纯随机场的Wick旋转
Wick rotation for holomorphic random fields
摘要：
路径作为全纯函数对欧氏时空的限制的随机场可以通过路径解析延拓进行Wick旋转。然后，关联函数的欧几里德对称性就变成相对论对称性。作为一个具体的例子，讨论了由量子场论激发的具有相互作用的卷积点过程。给出了一个构造具有铁磁相互作用的连续粒子系统的欧氏不变无穷体积测度的一般方案，并将其应用于所考虑的模型。与欧几里德量子场论，Widom-Rowlinson和Potts模型的连接被指出。对于给定的模型，路径解析连续和解析连续关联函数的存在，并暴露相对论对称性。
英文摘要：
Random field with paths given as restrictions of holomorphic functions to Euclidean space-time can be Wick-rotated by pathwise analytic continuation. Euclidean symmetries of the correlation functions then go over to relativistic symmetries. As a concrete example, convoluted point processes with interactions motivated from quantum field theory are discussed. A general scheme for the construction of Euclidean invariant infinite volume measures for systems of continuous particles with ferromagnetic interaction is given and applied to the models under consideration. Connections with Euclidean quantum field theory, Widom-Rowlinson and Potts models are pointed out. For the given models, pathwise analytic continuation and analytically continued correlation functions are shown to exist and to expose relativistic symmetries.
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