量子场论中的几种卷积
Some convolution products in Quantum Field Theory
摘要：
本文主要讨论了与量子场论重整化理论有关的几种概率模型的尺度依赖和相互作用的构造。我们首先回顾卷积产品的使用在Kreimer-Connes形式主义的微扰重整化。我们证明了Wilson有效作用量可以由场空间上正则化高斯测度的卷积乘积性质得到。然后，我们提出了一个自然的C*-代数框架尺度相关的场论，这可能会提高重整化理论的概念方法。本着同样的精神，我们介绍了一个概率的相互作用理论的简单模型的建设和应用它的量子场论通过定义一个配分函数在这种设置。
英文摘要：
This paper aims to show constructions of scale dependence and interaction on some probabilistic models which may be revelant for renormalization theory in Quantum Field Theory. We begin with a review of the convolution product's use in the Kreimer-Connes formalism of perturbative renormalization. We show that the Wilson effective action can be obtained from a convolution product propriety of regularized Gaussian measures on the space of fields. Then, we propose a natural C*-algebraic framework for scale dependent field theories which may enhance the conceptual approach to renormalization theory. In the same spirit, we introduce a probabilistic construction of interacting theories for simple models and apply it for quantum field theory by defining a partition function in this setting.
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