Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix
arXiv:hep-th/9608092 · doi:10.1016/S0550-3213(97)00358-1
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.
28 pages of LateX, removal of misprints and extension of the last section. more misprints corrected
References in corpus (3)
Cited by in corpus (11)
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