In this article a general relation between the short distance structure of quantum field theories and their phase space properties is exemplified by the simple class of generalized free fields. As is known, theories with decent phase space properties, resulting from a finite or moderately increasing infinite particle spectrum, always have non-trivial scaling (short distance) limits [cf. D. Buchholz and R. Verch, Rev. Math. Phys. 10, 775 (1998)]. But, whereas in the finite particle case the phase space properties of the limit theories comply with strong nuclearity conditions, they violate in the infinite particle case even rather mild compactness assumptions. These results provide further evidence to the effect that relevant information on the short distance structure of a theory can be obtained by phase space analysis. (C) 2002 American Institute of Physics. [References: 19]
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机译：在本文中，量子场论的短距离结构与其相空间特性之间的一般关系以广义自由场的简单类为例。众所周知，由有限的或适度增加的无限粒子光谱产生的具有适当相空间特性的理论，总是具有非平凡的缩放比例（短距离）限制。 D. Buchholz和R. Verch，Rev。Math。物理10，775（1998）]。但是，尽管在有限粒子情况下，极限理论的相空间特性符合强核条件，但在无限粒子情况下，甚至违反了相当紧凑的紧凑性假设。这些结果进一步证明了可以通过相空间分析获得有关理论的短距离结构的相关信息的效果。 （C）2002美国物理研究所。 [参考：19]
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