# Constructive aspects of algebraic euclidean field theory

February 17, 1999

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.

Keywords:

Euclidean quantum field theories, algebraic approach, constructive QFT