概率物理模型中相互作用的卷积积构造
Convolution product construction of interactions in probabilistic physical models
摘要：
本文的目的是给出一个概率结构的相互作用，这可能是相关的建设物理理论，如相互作用量子场论。我们从量子场论中配分函数的路径积分定义开始，它使我们想起了这个物理理论的概率性质。从一个被认为是自由理论的高斯定律出发，通过自由理论和一个也是概率定律的相互作用项之间的非平凡卷积积构造了一个相互作用理论。由此产生的理论，也是一个概率定律，表现出两个在现今的相互作用理论中已经存在的性质，如规范理论：相互作用项不依赖于自由项，两个不同的自由理论可以用同一个相互作用来实现。高斯测度的直接使用允许将本构造推广到配备高斯测度的无限维空间。
英文摘要：
This paper aims to give a probabilistic construction of interactions which may be relevant for building physical theories such as interacting quantum field theories. We start with the path integral definition of partition function in quantum field theory which recall us the probabilistic nature of this physical theory. From a Gaussian law considered as free theory, an interacting theory is constructed by nontrivial convolution product between the free theory and an interacting term which is also a probability law. The resulting theory, again a probability law, exhibits two proprieties already present in nowadays theories of interactions such as Gauge theory : the interaction term does not depend on the free term, and two different free theories can be implemented with the same interaction. The direct use of Gaussian measures allows to generalize the present construction for infinite dimensional spaces equipped with Gaussian measures.
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。
