Braided Structure in 4-dimensional conformal Quantum Field Theory

Higher dimensional conformal QFT possesses an interesting braided structure which, different from the d=1+1 models, is restricted to the timelike region and therefore easily escapes euclidean action methods. It lies behind the spectrum of anomalous dimensions which may be viewed as a kind of substitute for a missing particle interpretation in the presence of interactions.Comment: Dedicated to Gerhard Mack and Robert Schrader on the occasion of their 60th birthday, submitted to Phys. Lett. B, 10 pages, improvements of the formulation, shortening of the text, addition of a formula, removal of typo

Modular Localization and the Bootstrap-Formfactor Program

We extend the ''modular localization'' principle from free to interacting theories and test its power for the special class of d=1+1 factorizing models.Comment: 27 pages of Late

Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix

It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ''modular localization'' is not only useful in order to construct interaction-free nets of local algebras without using non-unique ''free field coordinates'', but also permits the study of properties of localization and braid-group statistics in low-dimensional QFT. It also sheds some light on the string-like localization properties of the 1939 Wigner's ''continuous spin'' representations.We formulate a constructive nonperturbative program to introduce interactions into such an approach based on the Tomita-Takesaki modular theory. The new aspect is the deep relation of the latter with the scattering operator.Comment: 28 pages of LateX, removal of misprints and extension of the last section. more misprints correcte