Dirk Schlingemann
Short-distance Analysis for Algebraic Euclidean Field Theory
Preprint series: ESI preprints

MSC:

81T05 Axiomatic quantum field theory; operator algebras

81T08 Constructive quantum field theory

81T17 Renormalization group methods

Abstract: Recently D. Buchholz and R. Verch have proposed a method for
implementing in algebraic quantum field theory ideas from
renormalization group analysis of short-distance (high energy)
behavior by passing to certain scaling limit theories.
Buchholz and Verch distinguish between different types of theories where the
limit is unique, degenerate, or classical, and the method allows in
principle to extract the `ultraparticle' content of a given model,
i.e. to identify particles (like quarks and gluons) that are not
visible at finite distances due to `confinement'. It is therefore of
great importance for the physical interpretation of the theory. The
method has been illustrated in a simple model in with some
rather surprising results.

This paper will focus on the question how the short distance
behavior of models defined by euclidean means is reflected in the
corresponding behavior of their Minkowski counterparts. More
specifically, we shall prove that if a euclidean theory has some
short distance limit, then it is possible to pass from this limit
theory to a theory on Minkowski space, which is a short distance limit
of the Minkowski space theory corresponding to the original euclidean
theory.
Keywords: Euclidean field theory, quantum field theory, constructive field theory, Osterwalder-Schrader reconstruction theorem, functional integral, statistical mechanics, renormalization group