Positivity in Rieffel's strict deformation quantization

TL;DR

This paper reviews a recent mathematical result on Rieffel's deformation quantization, demonstrating the continuity of states through deformation parameters and discussing its physical interpretation in quantum theory.

Contribution

It establishes the existence of continuous state sections in Rieffel's deformation, linking mathematical deformation to physical quantization.

Findings

States vary continuously with deformation parameter

Supports physical interpretation of deformation as quantization

Provides a framework for analyzing deformed C*-algebras

Abstract

We review a recent result on Rieffel's deformation quantization by actions of R^d: it is shown that for every state omega_0 of the undeformed C*-algebra A_0 there is a continuous section of states omega(hbar) through omega_0. We outline the physical interpretation in terms of quantization.