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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2013
    • (edited Jan 26th 2013)

    at renormalization I made the Definition-section have three different subsections, a new one of which is now Definition – Of theories in BV-CS form on Kevin Costello’s apprach. On the other hand, so far this contains mostly just a pointer to his article.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2013
    • (edited Jan 26th 2013)

    I started writing a summary of the key steps in Kevin Costello’s discussion of renormalization. At renormalization in the section Of theories in BV-CS form:

    1. The setup

    2. Operator (heat) kernels and propagators

    3. The renormalization group operator

    4. The path integral

    5. Renormalized action

    6. Renormalization

    The text still needs polishing and glue. You shouldn’t look at this right now if you don’t want to see an unfinished writeup. But I have to take a break now and get some dinner.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2017

    I have expanded the Idea-sections at renormalization and perturbative quantum field theory and added more references.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2018
    • (edited Jan 21st 2018)

    I am now beginning to spell out a comprehensive account at renormalization.

    To begin with, I added statement and proof that renormalization of time-ordered products is inductively in the arity given by extension of the corresponding distributions to the diagonal: here

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 31st 2018
    • (edited Jan 31st 2018)

    I have been compiling more material (from separate entries that I have been writing, with some glue added) on the rigorous formulation of renormalization in causal perturbation theory; in the section:

    Not done yet, but it is taking shape now.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2018

    I have now spelled out the proof of UV-regularization via counterterms, this prop..

    Hints for the idea this proof were offered DFKR 14, theorem A.1. I have tried to expand that out a little.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2018

    I have considerably further expanded the proof of that prop..

    In particular I made explicit (here) where the Hörmander topology in the definition of UV-cutoff (this def.) really enters.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2018

    Still on that prop. establishing UV-regularization by counterterms:

    Michael Dütsch kindly points out to me by private email that the afterthought of the proof, generalizing from one particular S-matrix to all of them, follows immediately by invoking again the main theorem. I have edited accordingly: paragraphs starting here

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2018

    just discovered (thanks to pointer from Igor Khavkine!) that what I thought now should exist has indeed already been developed: a genral theory of Feynman amplitudes recast from singular distributions on M nM^n to smooth functions on Fulton-MacPherson-type compactifications of configuration spaces of points (“wonderful compactifications”). Have added the following to the References-section here:

    An alternative to regarding propagators/time-ordered products/Feynman amplitudes as distributions of several variables with singularities at (in particular) coincident points, one may pullback these distributions to smooth functions on Fulton-MacPherson compactifications of configuration spaces of points and study renormalization in that perspective.

    This approach was originally considered specifically for Chern-Simons theory in

    which was re-amplified in

    A systematic development of perturbative quantum field theory from this perspective is discussed in

    For more see at Feynman amplitudes on compactified configuration spaces of points.

    diff, v106, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022

    added brief mentioning of Chern-Simons level renormalization (now here)

    diff, v112, current