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

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

2010-05-15

arxiv.org/abs/1005.2656v1

Commun.Math.Phys.304:95-123,2011

Physics

Mathematical Physics

34 pages

Scientific paper

10.1007/s00220-010-1137-1

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.

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