Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-08-18
Rev.Math.Phys. 10 (1998) 775-800
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, Latex
Scientific paper
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.
Buchholz Detlev
Verch Rainer
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