Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories

Autor(en)

Detlev Buchholz, Gandalf Lechner, Stephen J. Summers

Abstrakt

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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Georg-August-Universität Göttingen, University of Florida, Gainesville

Journal

Communications in Mathematical Physics

Band

304

Seiten

95-123

Anzahl der Seiten

29

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-010-1137-1

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/11bb2f4b-d44a-40c0-8270-3e402a7e945d