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nLab > Latest Changes: quantum observable

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 11th 2013

    at quantum observable there used to be just the definition of geometric prequantum observables. I have added a tad more.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2023

    added pointer to:

    here and in related entries (such as at quantum state space)

    diff, v20, current

    • CommentRowNumber3.
    • CommentAuthorperezl.alonso
    • CommentTimeMar 24th 2025

    As discussed elsewhere, one can obtain (higher) topological observables by computing the Pontriagin homology ring. I suppose the particular case of WZW models does not need the space to have a circle factor. To incorporate the gerbe I guess one has to consider fields valued in the higher group extension determined by the gerbe class. But how does one incorporate the kinetic term so as to see the WZW observables?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 25th 2025

    The observables obtained as the Pontrjagin algebra of the mapping space to a flux classifying space are to be thought of as the observables on “topological flux sectors” of a higher gauge theory. The WZW model is not directly an example of such theories.

    But 3D abelian Chern-Simons theory is, with the CS Lagrangian density regarded as the higher flux density H3 of a twisted gerbe, satisfying the Bianchi identity dH3=F2F2, dF2=0. An evident choice of flux quantization law for these Bianchi identities is that classified by the 2-sphere S2.

    And one finds that the Pontrjagin algebras of Maps*((Σ2×ℝ)∪{∞},S2) indeed know about the modular functor of 3D abelian CS theory and as such about the conformal blocks and the modularity of the abelian WZW model!

    The details of this statement are currently in section 4.2 of the draft with the long title Understanding Topological Quantum Gates in FQH Systems via the Algebraic Topology of exotic Flux Quantization.

    • CommentRowNumber5.
    • CommentAuthorperezl.alonso
    • CommentTimeMar 25th 2025

    Ah I was unaware of this draft, thanks!

  6. A couple of typos from the draft:

    taditionally; intermedite

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime3 days ago

    Thanks!, I’ll fix it once the Overleaf server comes back online (has been down for over an hour now).

    Meanwhile, I have also been working on slides for a 5-minute Ignite-style presentation of the matter (here) aimed at the AI-inclined audience in London.

  8. Wow, 20 slides 15 seconds each, they say. Or will you go for the 15 slides 20 seconds each version?

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime2 days ago

    I’ll stick with 15 slides (will eventually add overlay dynamics, though), since I may have less than 5 min even.

    It’s not clear to me whether the presentation is going to strictly be in Ignite-format (with auto-advancing slides) — but content-wise the talks currently go through Ignite “coaching”. :-)

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