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Warped convolutions, rieffel deformations and the construction of quantum field theories

Buchholz, Detlev, Lechner, Gandalf and Summers, Stephen J. 2010. Warped convolutions, rieffel deformations and the construction of quantum field theories. Communications in Mathematical Physics 304 (1) , pp. 95-123. 10.1007/s00220-010-1137-1

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Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel’s strict deformations of C *–dynamical systems with automorphic actions of R n , whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita–Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 0010-3616
Last Modified: 04 Jun 2017 08:09

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