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arXiv · hep-th/9608092

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

B. Schroer
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Abstract

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.

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B. Schroer. 1997-03-25. Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix. https://doi.org/10.1016/s0550-3213(97)00358-1

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