Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
Buchholz D, Lechner G, Summers SJ (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Book Volume: 304
Pages Range: 95-123
Journal Issue: 1
DOI: 10.1007/s00220-010-1137-1
Abstract
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 ℝn, 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. © 2010 The Author(s).
Authors with CRIS profile
Additional Organisation(s)
Involved external institutions
University of Florida
United States (USA) (US)
Georg-August-Universität Göttingen
Germany (DE)
Universität Wien / University of Vienna
Austria (AT)
United States (USA) (US)
Georg-August-Universität Göttingen
Germany (DE)
Universität Wien / University of Vienna
Austria (AT)
How to cite
APA:
Buchholz, D., Lechner, G., & Summers, S.J. (2011). Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories. Communications in Mathematical Physics, 304(1), 95-123. https://dx.doi.org/10.1007/s00220-010-1137-1
MLA:
Buchholz, Detlev, Gandalf Lechner, and Stephen J. Summers. "Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories." Communications in Mathematical Physics 304.1 (2011): 95-123.
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