Warped Convolutions,Rieffel Deformations and the Construction of Quantum Field Theories |
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Authors: | Detlev Buchholz Gandalf Lechner Stephen J Summers |
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Institution: | 1.Institut für Theoretische Physik and Courant Centre “Higher Order Structures in Mathematics”,Universit?t G?ttingen,G?ttingen,Germany;2.Fakult?t für Physik,Universit?t Wien,Vienna,Austria;3.Department of Mathematics,University of Florida,Gainesville,USA |
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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
\mathbb Rn{\mathbb 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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