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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2010

    took me until now to realize that Kevin Costello and Owen Gwilliam have a wiki on their work on factorization algebras:

    Factorization algebras in perturbative quantum field theory

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 26th 2010

    Amazing!

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeNov 26th 2010

    By the way, Kontsevich gave a talk on June 17 (Institut Camille Jordan (Lyon) June 16 - 18, 2010)

    If anybody has notes it woudl be nice to see. As far as I heard from the speaker (this May) it is about the L-infinity structure on sections of n-shifted (in the sense of cochain complexes) sheaf of local fields tensored by densities on the manifold. The claim is that this L-infinity structure is an expression of OPE-s and that it controls the deformations. Thus the perturbative QFT follows as a case of deformation theory. The advantage is that the initial undeformed case may be rather general. It is like in QM: you start with a solvable case of QM and do perturbations around it, never mind how complicated the original point is. Usual setups (including the one in Costello’s book) require quadratic potential as the origin around which one expands the higher order terms. E. g. some perturbation series even if expressed in this form do not converge while viewed as perturbations over some other initial points do.

    Maxim Kontsevich - Renormalization via OPE

    I’ll describe an approach to renormalization of a QFT given as a bundle of local fields on the space-time, together with an operator product expansion.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2017
    • (edited Sep 7th 2017)

    [seven years later…]

    Kontsevich gave a talk on June 17 (Institut Camille Jordan (Lyon) June 16 - 18, 2010)

    BTW, the conference page is still here

    The claim is that this L-infinity structure is an expression of OPE-s and that it controls the deformations.

    I have a vague memory that you had told me about this back then. Do you happen to still have copy of any notes or any other details?