Complete Positivity of Rieffel's Deformation Quantization by Actions of ${\mathbb{R}}^d$

Abstract

In this paper we consider C*-algebraic deformations a la Rieffel and show that every state of the undeformed algebra can be deformed into a state of the deformed algebra in the sense of a continuous field of states. The construction is explicit and involves a convolution operator with a particular Gauss function.

17 pages. New (more precise) title and other minor changes. Final version

References in corpus (2)

• Deformation quantization of Poisson manifolds, I
• Macroscopic observables and the Born rule

Cited by in corpus (4)

• Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
• Smooth crossed products of Rieffel's deformations
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• Deformation Quantization of a Certain Type of Open Systems