Modular intersections of von-Neumann-algebras in quantum field theory

We show that modular intersections of von-Neumann-algebras occur naturally in 2+1-dim. quantum field theory. An example is given by the local observable algebras of wedge regions with a common lightray in the vacuum sector. Conversely, starting with a set of four algebras lying in a specified modular position relative to each other we construct a net of local observables of a 2+1 dim. quantum field theory. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(193) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Symmetries and modular intersections of von-Neumann-algebras

SIGLEAvailable from TIB Hannover: RR 1596(192) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Modular constructions of quantum field theories with interactions

We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of 'quantum localization' (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free) generators of these wedge algebras. These generators are 'on-shell'- and their Fourier transforms turn out to fulfill the Zamolodchikov-Faddeev algebra. As the wedge algebras contain the crossing symmetry informations, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(365) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Extensions of conformal nets and superselection structures

Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and coronal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2, R), showing that they violate 3-regularity for n>2. When n#>=#2, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net. (orig.)Available from TIB Hannover: RR 1596(255) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman