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

TL;DR

This paper explores how warped convolutions serve as a constructive method to deform quantum field theories via Rieffel's strict deformation, maintaining key physical properties while enabling new inequivalent models.

Contribution

It demonstrates that warped convolutions realize Rieffel deformations in quantum physics and can be adapted to Minkowski space, producing physically consistent but inequivalent quantum field theories.

Findings

Warped convolutions provide isometric representations of Rieffel deformations.

Deformed theories preserve modular data of original theories.

Deformed theories are physically consistent and inequivalent to original models.

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.