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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 12th 2012
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJul 12th 2012

My impression is that you are here talking about a particular construction of strict deformation of Rieffel which takes polarization as part of the input. On the other hand, Rieffel’s defining of strict quantization is just a C-star algebraic deformation with strong properties enough to be sensible for C-star framework. I assume that the entry could in principle be about the general case, while Landsman has geometric-like case which is a richer case, still satisfying the general framework. But maybe I am wrong.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 12th 2012

That sounds good. I just briefly looked at my old notes. I haven’t actually looked at Rieffel’s stuff. If you have it in reach, please add it to the entry!

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeJul 12th 2012
• (edited Jul 12th 2012)

I know that he has invented the concept in late 1980-s, but the earliest reference I can find on MathSciNet on this seems to be

• Marc Rieffel, Deformation quantization and operator algebras, in: Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988), 411–423, Proc. Sympos. Pure Math., 51, Part 1, Amer. Math. Soc. 1990, MR91h:46120

and then

• Marc Rieffel, Deformation quantization for actions of $\mathbb{R}^d$, Mem. Amer. Math. Soc. 106 (1993), no. 506, x+93 pp. MR94d:46072
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 12th 2012

Thanks!!

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 12th 2012

Did you see that Rieffel has these and more as pdf-s linked from his webpage?

I have added one more reference to the entry, taken from there.

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeJul 12th 2012

Thank you, as well!I did not look at his page for quite a while…

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 12th 2017

I have expanded the Idea-section at strict deformation quantization a bit more; also the Idea-section at non-perturbative quantum field theory.