A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras
A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras
复制标题
重正化群方法。
DOI：
10.1007/s10955-014-1163-z
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发表时间：
2014
影响因子：
1.6
通讯作者：
G. Slade
中科院分区：
文献类型：
--
作者：
D. Brydges;G. Slade
本文是第一个系列致力于发展一个严格的重整化群方法涉及玻色子场，费米子场，或两者的晶格场理论。我们的直接动机是一个特定的模型，涉及玻色子和费米子场，它作为连续时间弱自回避行走的代表出现。在本文中，我们定义了赋范代数适用于重整化群分析，并开发了对这些代数进行分析的方法。我们还发展了这些赋范代数上的高斯积分理论，并证明了高斯积分的估计。这里发展的概念和结果为继续本系列后续论文中提出的方法提供了基础。
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving both boson and fermion fields, which arises as a representation of the continuous-time weakly self-avoiding walk. In this paper, we define normed algebras suitable for a renormalisation group analysis, and develop methods for performing analysis on these algebras. We also develop the theory of Gaussian integration on these normed algebras, and prove estimates for Gaussian integrals. The concepts and results developed here provide a foundation for the continuation of the method presented in subsequent papers in the series.