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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 20th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for: * [[Stefan Waldmann]], _Poisson-Geometrie und Deformationsquantisierung_, Springer (2007) &lbrack;[doi:10.1007/978-3-540-72518-3](https://doi.org/10.1007/978-3-540-72518-3)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/C%2A+algebraic+deformation+quantization/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/C%2A+algebraic+deformation+quantization/20">v20</a>, <a href="https://ncatlab.org/nlab/show/C%2A+algebraic+deformation+quantization">current</a>

   added publication data for:

   • Stefan Waldmann, Poisson-Geometrie und Deformationsquantisierung, Springer (2007) [doi:10.1007/978-3-540-72518-3]

   diff, v20, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 20th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded the Idea-section ([here](https://ncatlab.org/nlab/show/C*+algebraic+deformation+quantization#Idea)) by paragraphs adapted from what I just wrote into the new entry *[[deformation quantization]]* and adding explicit pointers both to converging formal deformation quantization (which I have given its own References-subsection, [here](https://ncatlab.org/nlab/show/C*+algebraic+deformation+quantization#ConvergingFormalDeformationQuantization)) as well as for the zoo of $C^\ast$-algebraic strict deformation quantizations, which is nicely surveyed in Section 2 of [Hawkins (2008a)](https://ncatlab.org/nlab/show/C*+algebraic+deformation+quantization#Hawkins08a). I feel the terminology "deformation quantization" for all these notions is (a) not non-standard (Hawkins uses it extensively) and (b) well justified on conceptual grounds and (c) it should no longer be ambiguous with these edits and the new disambiguation page *[[deformation quantization]]*. But of course, if you spot further passages that still seem ambiguous or misleading, then let's expand further. <a href="https://ncatlab.org/nlab/revision/diff/C%2A+algebraic+deformation+quantization/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/C%2A+algebraic+deformation+quantization/21">v21</a>, <a href="https://ncatlab.org/nlab/show/C%2A+algebraic+deformation+quantization">current</a>

   I have expanded the Idea-section (here) by paragraphs adapted from what I just wrote into the new entry deformation quantization and adding explicit pointers both to converging formal deformation quantization (which I have given its own References-subsection, here) as well as for the zoo of $C^\ast$-algebraic strict deformation quantizations, which is nicely surveyed in Section 2 of Hawkins (2008a).

   I feel the terminology “deformation quantization” for all these notions is (a) not non-standard (Hawkins uses it extensively) and (b) well justified on conceptual grounds and (c) it should no longer be ambiguous with these edits and the new disambiguation page deformation quantization.

   But of course, if you spot further passages that still seem ambiguous or misleading, then let’s expand further.

   diff, v21, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded these pointers on [[group algebras]] of ([[underlying]] [[discrete group|discrete]]) [[Heisenberg groups]] as [[strict deformation quantizations]] of [[presymplectic manifold|pre-]][[symplectic vector spaces|symplectic]] [[topological vector spaces]] by [[continuous field of C-star algebras|continuous fields of]] [[Weyl algebras]]: * [[Ernst Binz]], [[Reinhard Honegger]], [[Alfred Rieckers]], *Infinite dimensional Heisenberg group algebra and field-theoretic strict deformation quantization*, International Journal of Pure and Applied Mathematics **38** 1 (2007) &lbrack;[ijpam:2007-38-1/6](https://ijpam.eu/contents/2007-38-1/6/index.html), [pdf](https://www.ijpam.eu/contents/2007-38-1/6/6.pdf)&rbrack; * [[Reinhard Honegger]], [[Alfred Rieckers]], *Heisenberg Group Algebra and Strict Weyl Quantization*, Chapter 23 in: *Photons in Fock Space and Beyond, Volume I: From Classical to Quantized Radiation Systems*, World Scientific (2015) &lbrack;chapter:[doi;10.1142/9789814696586_0023](https://doi.org/10.1142/9789814696586_0023), book:[doi:10.1142/9251-vol1](https://doi.org/10.1142/9251-vol1)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/C%2A+algebraic+deformation+quantization/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/C%2A+algebraic+deformation+quantization/22">v22</a>, <a href="https://ncatlab.org/nlab/show/C%2A+algebraic+deformation+quantization">current</a>

   added these pointers

   on group algebras of (underlying discrete) Heisenberg groups as strict deformation quantizations of pre-symplectic topological vector spaces by continuous fields of Weyl algebras:

   • Ernst Binz, Reinhard Honegger, Alfred Rieckers, Infinite dimensional Heisenberg group algebra and field-theoretic strict deformation quantization, International Journal of Pure and Applied Mathematics 38 1 (2007) [ijpam:2007-38-1/6, pdf]

   • Reinhard Honegger, Alfred Rieckers, Heisenberg Group Algebra and Strict Weyl Quantization, Chapter 23 in: Photons in Fock Space and Beyond, Volume I: From Classical to Quantized Radiation Systems, World Scientific (2015) [chapter:doi;10.1142/9789814696586_0023, book:doi:10.1142/9251-vol1]

   diff, v22, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso this one: * [[Ernst Binz]], [[Reinhard Honegger]], [[Alfred Rieckers]], *Field-theoretic Weyl Quantization as a Strict and Continuous Deformation Quantization*, Annales Henri Poincaré **5** (2004) 327–346 &lbrack;[doi:10.1007/s00023-004-0171-y](https://doi.org/10.1007/s00023-004-0171-y)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/C%2A+algebraic+deformation+quantization/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/C%2A+algebraic+deformation+quantization/22">v22</a>, <a href="https://ncatlab.org/nlab/show/C%2A+algebraic+deformation+quantization">current</a>

   also this one:

   • Ernst Binz, Reinhard Honegger, Alfred Rieckers, Field-theoretic Weyl Quantization as a Strict and Continuous Deformation Quantization, Annales Henri Poincaré 5 (2004) 327–346 [doi:10.1007/s00023-004-0171-y]

   diff, v22, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexfinally added the original reference: * [[Marc A. Rieffel]], *Deformation quantization of Heisenberg manifolds*, Communications in Mathematical Physics **122** (1989) 531–562 &lbrack;[doi:10.1007/BF01256492](https://doi.org/10.1007/BF01256492)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/C%2A+algebraic+deformation+quantization/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/C%2A+algebraic+deformation+quantization/27">v27</a>, <a href="https://ncatlab.org/nlab/show/C%2A+algebraic+deformation+quantization">current</a>

   finally added the original reference:

   • Marc A. Rieffel, Deformation quantization of Heisenberg manifolds, Communications in Mathematical Physics 122 (1989) 531–562 [doi:10.1007/BF01256492]

   diff, v27, current