Constructive aspects of algebraic euclidean field theory

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.