# Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples

August 18, 1997

The concept of scaling algebra provides a novel framework for the general
structural analysis and classification of the short distance properties of
algebras of local observables in relativistic quantum field theory. In the
present article this method is applied to the simple example of massive free
field theory in s = 1,2 and 3 spatial dimensions. Not quite unexpectedly, one
obtains for s = 2,3 in the scaling (short distance) limit the algebra of local
observables in massless free field theory. The case s =1 offers, however, some
surprises. There the algebra of observables acquires in the scaling limit a
non-trivial center and describes charged physical states satisfying Gauss' law.
The latter result is of relevance for the interpretation of the Schwinger model
at short distances and illustrates the conceptual and computational virtues of
the method.

open access link

Rev.Math.Phys. 10 (1998) 775-800

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