A renormalisation group method. II. Approximation by local polynomials

Abstract

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 $T_{\varphi }$ semi-norm introduced in part I of the series.

30 pages

References in corpus (5)

• Functional integral representations for self-avoiding walk
• A renormalisation group method. III. Perturbative analysis
• A renormalisation group method. IV. Stability analysis
• A renormalisation group method. I. Gaussian integration and normed algebras
• A renormalisation group method. V. A single renormalisation group step

Cited by in corpus (4)

• A renormalisation group method. III. Perturbative analysis
• A renormalisation group method. IV. Stability analysis
• A renormalisation group method. I. Gaussian integration and normed algebras
• A renormalisation group method. V. A single renormalisation group step