%0 Journal Article
%T A renormalisation group method. II. Approximation by local polynomials
%A David C. Brydges
%A Gordon Slade
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s10955-014-1164-y
%X 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 $T_{\phi}$ semi-norm introduced in part I of the series.
%U http://arxiv.org/abs/1403.7253v2