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Deformation quantization (survey, introduction, sources)

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  1. Aug 18, 2014 #1

    marcus

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    Dearly Missed

    In case anyone is interested in DQ I came across this, which is moderately accessible in parts.
    http://math.berkeley.edu/~alanw/242papers99/karaali.pdf

    Evidently Alan Weinstein (Berkeley faculty) was teaching a graduate course Math 242 back in 1999 and put this online for his students.

    If anyone likes this approach to quantization and has helpful source material please post it here.
    Also Keraali has an interesting list of sources at the end of his survey.

    I have some other links somewhere, and will go fetch them.
    http://www.math.columbia.edu/~woit/wordpress/?p=7108&cpage=1#comment-214180
    http://www.math.columbia.edu/~woit/wordpress/?p=7108&cpage=1#comment-214186
    http://en.wikipedia.org/wiki/Wigner–Weyl_transform#Deformation_quantization

    http://ncatlab.org/nlab/show/deformation+quantization

    http://arxiv.org/abs/math/9809056
    Deformation Quantization: Twenty Years After
    Daniel Sternheimer
    (Submitted on 10 Sep 1998)
    We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe...
     
    Last edited: Aug 18, 2014
  2. jcsd
  3. Aug 20, 2014 #2
    Formal deformation quantization of Poisson manifolds

    Dear Marcus,
    interesting thread.
    Deformation quantization is strongly connecetd with the work of Kontsevich, see
    http://en.wikipedia.org/wiki/Kontsevich_quantization_formula (he won the Fields medal for it). It means that (at least from the fomal point of view) any Poisson manifold can be qunatized using deformation quantization.

    I used a result of Tureav: the space of all holonomies on a surfaces (2D) can be quantized by deformation quantization, one obtains the skein space (3D) (space of singular knots) and the deformation parameter (Plancks constant) changes to a space dimension.

    Torsten
     
  4. Aug 20, 2014 #3

    kith

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    A while ago I downloaded the following pedagogical introduction but I haven't found the time to read it yet.

    "Deformation quantization in the teaching of quantum mechanics"
    Allen C. Hirshfeld and Peter Henselder
    Am. J. Phys. 70 (5), May 2002
    http://arXiv.org/abs/quant-ph/0208163v1
     
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