重正化群方法。II。局部多项式逼近
A renormalisation group method. II. Approximation by local polynomials
摘要：
本文是第二次在一系列致力于发展一个严格的重整化群方法格场论涉及玻色子场，费米子场，或两者兼而有之。该方法设置在一个赋范代数$\mathcal{N}$的域的泛函。本文提出了一种用域上的局部多项式逼近$\mathcal{N}$中元素的一般方法--局部化法。从重整化组的观点来看，在$\mathcal{N}$中构造对应于$F$的局部多项式相当于提取$F$的相关部分和边缘部分。我们证明估计有关$F$和相应的本地多项式，在$T_ϕ$半规范介绍了第一部分的系列。
英文摘要：
This paper is the second 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 method is set within a normed algebra $\mathcal{N}$ of functionals of the fields. In this paper, we develop a general method---localisation---to approximate an element of $\mathcal{N}$ by a local polynomial in the fields. From the point of view of the renormalisation group, the construction of the local polynomial corresponding to $F$ in $\mathcal{N}$ amounts to the extraction of the relevant and marginal parts of $F$. We prove estimates relating $F$ and its corresponding local polynomial, in terms of the $T_ϕ$ semi-norm introduced in part I of the series.
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