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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:

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 $M^n$ 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