The Algebra of Block Spin Renormalization Group Transformations

TL;DR

This paper explores the algebraic structure of block spin renormalization group transformations, providing abstract derivations of key identities used in analyzing symmetry breaking in many Boson systems.

Contribution

It introduces an abstract algebraic framework for block spin RG transformations, deriving fundamental identities like composition rules and relations between critical and background fields.

Findings

Derived composition rule for RG transformations

Established relation between critical and background fields

Provided algebraic perspective on symmetry breaking analysis

Abstract

Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. In this paper, we discuss some of its purely algebraic aspects in an abstract setting. For example, we derive some "well known" identities like the composition rule and the relation between critical fields and background fields.