SCALING ALGEBRAS AND RENORMALIZATION-GROUP IN ALGEBRAIC QUANTUM-FIELDTHEORY - II - INSTRUCTIVE EXAMPLES

The concept of scaling algebra provides a novel framework for the gene ral structural analysis and classification of the short distance prope rties of algebras of local observables in relativistic quantum field t heory. In the present article this method is applied to the simple exa mple of massive free held 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 fie ld theory. The case s = 1 offers, however, some surprises. There the a lgebra of observables acquires in the scaling limit a non-trivial cent er and describes charged physical states satisfying Gauss' law. The la tter result is of relevance for the interpretation of the Schwinger mo del at short distances and illustrates the conceptual and computationa l virtues of the method.