Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories accessible adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory kan lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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 d\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.