Constructive aspects of algebraic euclidean field theory

TL;DR

This paper develops a C*-algebraic framework for lattice Euclidean field theory, enabling the analysis of continuum limits with desirable properties like reflection positivity and translation invariance, bridging constructive and axiomatic approaches.

Contribution

It introduces a C*-algebraic approach to lattice field theory, integrating constructive and axiomatic methods to identify model-independent features of Euclidean field theories.

Findings

Generalized block spin transformations within C*-algebraic setup

Established continuum limits satisfying reflection positivity

Provided a guideline for constructing Euclidean field theory models

Abstract

This paper is concerned with constructive and structural aspects of euclidean field theory. We present a C*-algebraic approach to lattice field theory. Concepts like block spin transformations, action, effective action, and continuum limits are generalized and reformulated within the C*-algebraic setup. Our approach allows to relate to each family of lattice models a set of continuum limits which satisfies reflexion positivity and translation invariance which suggests a guideline for constructing euclidean field theory models. The main purpose of the present paper is to combine the concepts of constructive field theory with the axiomatic framework of algebraic euclidean field theory in order to separate model independent aspects from model specific properties.