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

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 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.

34 pages

References in corpus (3)

• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• Deformations of quantum field theories on spacetimes with Killing vector fields
• Complete Positivity of Rieffel's Deformation Quantization by Actions of ${\mathbb{R}}^d$

Cited by in corpus (6)

• Deformations of quantum field theories on spacetimes with Killing vector fields
• An operator expansion for integrable quantum field theories
• Deformations of Fermionic Quantum Field Theories and Integrable Models
• Reflection positivity for the circle group
• Wedge-Local Quantum Fields on a Nonconstant Noncommutative Spacetime
• Relativistic Corrections to the Moyal-Weyl Spacetime