Wigner representation theory of the Poincaré group, localization, statistics and the S-matrix
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 non-perturbative 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.
- Publication:
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Nuclear Physics B
- Pub Date:
- February 1997
- DOI:
- 10.1016/S0550-3213(97)00358-1
- arXiv:
- arXiv:hep-th/9608092
- Bibcode:
- 1997NuPhB.499..519S
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 28 pages of LateX, removal of misprints and extension of the last section. more misprints corrected