Positivity in Rieffel’s strict deformation quantization. (English) Zbl 1203.81086

Waldmann, Stefan

Exner, Pavel (ed.), XVIth international congress on mathematical physics, Prague, Czech Republic, August 3–8, 2009. With DVD. Hackensack, NJ: World Scientific (ISBN 978-981-4304-62-7/hbk). 509-513 (2010).

Summary: We review a recent result on Rieffel’s deformation quantization by actions of \(\mathbb R^d\): it is shown that for every state \(\omega_0\) of the undeformed \(C^*\)-algebra there is a continuous section of states \(\omega(\hbar)\) through \(\omega_0\). We outline the physical interpretation in terms of quantization.
For the entire collection see [Zbl 1192.00040].

MSC:

81S10	Geometry and quantization, symplectic methods
53D55	Deformation quantization, star products
46L60	Applications of selfadjoint operator algebras to physics

Keywords:

Rieffel deformation quantization; positive deformation