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

Abstract

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.

arXiv comment25 pages, Latex

References in corpus (2)

• Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory
• Phase Space Properties of Local Observables and Structure of Scaling Limits

Cited by in corpus (16)

• The Quest for Understanding in Relativistic Quantum Physics
• Dynamical locality of the free scalar field
• Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
• Scaling limits of integrable quantum field theories
• Scaling limits of lattice quantum fields by wavelets
• Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
• On dilation symmetries arising from scaling limits
• Scaling Algebras and Superselection Sectors: Study of a Class of Models
• Quantum massless field in 1+1 dimensions
• Structure functions of the 2d O(n) non-linear sigma models
• Structure functions of 2d integrable asymptotically free models
• Localizable Particles in the Classical Limit of Quantum Field Theory
• Extensions of Bundles of C*-algebras
• Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models
• The Structure of Charges in the Ultraviolet and an Intrinsic Notion of Confinement
• Infinite volume limits in Euclidean quantum field theory via stereographic projection