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Zbl 0672.22022
Baumgärtel, Hellmut
On nets of local algebras on ${\bbfZ}\sp 4$, covariant with respect to the discrete Poincaré group; causality and scattering theory. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 48, No.4, 311-323 (1988). ISSN 0246-0211

Summary: The paper contains constructions of nets of local algebras on ${\bbfZ}\sp 4$, which are covariant with respect to the discrete Poincaré group ${\cal P}$, using CCR-Weyl-algebras over phase spaces depending on a certain measure. Firstly, there are causal nets in this framework. Secondly, under a certain assumption on the measure, one can apply methods developed in the paper [Commun. Math. Phys. 94, 331-352 (1984; Zbl 0578.47007)] and in related papers to establish a ${\cal P}$- covariant perturbation theory with convergent LSZ-scattering process.

MSC 2000:: *22E70 Appl. of Lie groups to physics
46N99 Appl. of functional analysis
47A40 Scattering theory of linear operators
81T08 Constructive quantum field theory

Keywords: nets of local algebras; Poincaré group; CCR-Weyl-algebras; phase spaces; LSZ-scattering process

Citations: Zbl 0578.47007

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