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nLab > Latest Changes: orbit method

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2012
    • (edited Dec 28th 2012)

    I have tried to expand the Idea-section at orbit method a little.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2012

    also added further references to orbit method, including a pointer to Bruce Bartlett’s generalization to 2-group 2-representation.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 28th 2012

    I have added to the references at orbit method and Wilson loop a pointer to section 4 of

    • Chris Beasley, Localization for Wilson Loops in Chern-Simons Theory (arXiv:0911.2687)

    as a reference for details on how the Wilson loop observable is re-expressed as a path integral.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2012
    • (edited Dec 29th 2012)

    I have been adding some basic Definitions and constructions to orbit method, (but didn’t get to the main statement yet).

    Then I started a section Formulation in higher geometry with some remarks on how these structures arise naturally from certain universal constructions on differential moduli stacks (with an eye towards applications in extended Chern-Simons theory with Wilson loop defects…)

    This is still under construction. Don’t look at it yet if you don’t want to see imperfections.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 30th 2012
    • (edited Dec 30th 2012)

    Presumably you saw Chern-Simons Theory with Wilson Lines and Boundary in the BV-BFV Formalism. Lots of orbits going on there.

    Oh yes, you did.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 30th 2012

    Hi David,

    the formulation of Wilson loops by the orbit method is indicated already in Witten’s original article. The basic idea goes back to (at least) an article form 1978. The recent article that you point to discusses aspects of this in the context of BV-BRST formalism.

    I have started to add some comments and some pointers to the literature at Chern-Simons theory – With Wilson line observables.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 30th 2012
    • (edited Dec 30th 2012)

    Have expanded further at orbit method. There is now a section reviewing traditional material:

    and a section refining this to higher geometry:

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2013

  9. Added a quick explanation of the relation of an integral symplectic form to the prequantum line bundle.

    Anonymous

    diff, v38, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2021

    Thanks. I have now made your requested pointer Bohr--Sommerfeld condition redirect to the existing entry Bohr-Sommerfeld leaf (though the actual relation between Bohr-Sommerfeld and integrality of the symplectic form might need to be expanded on…)

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2023

    have touched typesetting, formatting and wording in various places, for streamlining.

    diff, v40, current

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