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

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
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