ep - t h / 96 08 09 2 v 3 2 5 M ar 1 99 7 Wigner Representation Theory of the Poincaré Group , Localization , Statistics and the S - Matrix Bert Schroer Freie

ep - t h / 96 08 09 2 v 1 1 4 A ug 1 99 6 Notes on the Wigner Representation Theory of the Poicaré Group , Localization and Statistics

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 framework was recently used by Brunetti, Guido and Longo in order to construct interaction-free nets of local algebras without using non-unique ”free field coordinates”. It is shown that this ...

ar X iv : h ep - t h / 98 05 09 3 v 1 1 5 M ay 1 99 8 A Course on : “ Modular Localization and Nonperturbative Local Quantum Physics ”

ar X iv : h ep - t h / 97 07 23 0 v 1 2 8 Ju l 1 99 7 A Course on : “ Quantum Field

ar X iv : h ep - t h / 94 12 09 9 v 1 1 2 D ec 1 99 4 Poisson Poincaré groups

We present almost complete list of normal forms of classical r-matrices on the Poincaré group.

ar X iv : h ep - t h / 93 10 05 4 v 2 3 F eb 1 99 4 Hilbert Spaces for Nonrelativistic and Relativistic “ Free ” Plektons ( Particles with Braid Group Statistics ) ∗

Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of n “free” nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the Galilei group and a unitary representation of the Poincaré group respectively. In the relativistic case we also discuss the situation where the braid group is r...