A Renormalisation Group Method. IV. Stability Analysis
A Renormalisation Group Method. IV. Stability Analysis
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重正化群方法。
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
G. Slade
中科院分区：
文献类型：
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作者：
D. Brydges;G. Slade
本文是第四次在一系列致力于发展一个严格的重整化群方法格场理论涉及玻色子领域，费米子领域，或两者兼而有之。第三篇论文在该系列提出了一个微扰分析的超对称场理论，代表了连续时间弱自避免行走$${{mathbb Z}}^d }$$Zd。我们现在提出一个分析的相关相互作用泛函的超对称场论，它允许非微扰分析进行的临界尺寸$$d = 4$$d=4。本文的结果包括：相互作用的稳定性的证明，估计，使控制高斯期望涉及玻色子和费米子领域，估计绑定的扰动分析中的错误，和一个关键的收缩估计，以处理无关的方向流的重整化组。这些结果是必不可少的分析一般重整化组步骤中的第五篇论文中的系列。
This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on $${{{mathbb Z}}^d }$$Zd. We now present an analysis of the relevant interaction functional of the supersymmetric field theory, which permits a nonperturbative analysis to be carried out in the critical dimension $$d = 4$$d=4. The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. These results are essential for the analysis of the general renormalisation group step in the fifth paper in the series.