服从二次交换关系的量子场的广义函数
Generalized functions for quantum fields obeying quadratic exchange relations
摘要：
根据后来的发展，重新研究了20世纪50年代量子场论（QFT）中定义为算符值Schwartz分布的场的公理化表述。这些包括，在物理方面，建设了丰富的（2维）可溶性QFT模型与二次交换关系，并在数学方面，广义函数的Colombeau代数的介绍。利用这一事实，即能量的积极性产生了一个自然的正则化的Wightman分布的解析函数在管域中，我们认为，灵活的概念Colombeau理论，可以利用特定的正则化更适合（比施瓦茨分布）的数学公式的QFT。
英文摘要：
The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the construction of a wealth of (2-dimensional) soluble QFT models with quadratic exchange relations, and, on the mathematical side, the introduction of the Colombeau algebras of generalized functions. Exploiting the fact that energy positivity gives rise to a natural regularization of Wightman distributions as analytic functions in a tube domain, we argue that the flexible notions of Colombeau theory which can exploit particular regularizations is better suited (than Schwartz distributions) for a mathematical formulation of QFT.
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