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Before we had the n-Forum, I tried to start a discussion on the nLab on the subject of Kantization
It quickly became obvious that the nLab is not a great place to have a discussion, but now that we have the n-Forum, I thought I would try again here.
If someone could help by giving a roadmap of concepts I need to learn before I can grok Kantization, I’d appreciate it.
Recently, Johan Alm wrote a very neat paper
The paper proves an aspect of
suggested by Urs Schreiber. A summary of Alm’s paper with many motivating references is provided here.
This page represents an experiment similar to the Journal Club’s effort to understand the papers
IntTrans David Ben-Zvi, John Francis, David Nadler, Integral transforms and Drinfeld Centers in Derived Geometry (arXiv)
CharTheo David Ben-Zvi, David Nadler, The Character Theory of a Complex Group (arXiv)
The goal is to build up, step-by-step, the background knowledge required to understand Alm’s paper. The finite model considered is simple enough that we hope to advance our understanding of elementary concepts that are mostly taken for granted by the experts here at n-Headquarters.
When we are done, we hope to have a complete, self-contained presentation that should be accessible to mildly sophisticated undergraduate physics and mathematics students.
We also hope that the experts will keep an eye on us and when we get stuck, might gently nudge us in the right direction. As always, this page is open to all. Any questions or contributions are more than welcome.
Most of the entry is still a long discussion between Eric and others on a concept of Kan extension per se. I'd like to have that discussion separated into nForum and then the entry expanded more toward the very Kantization idea. (So far I am not competent to write it.)
As far as the general topic of Feynman path integrals I have uploaded the rarely available proceedings article of Robbin and Salamon as RobbinSalamonPhaseFunctionsPathIntegrals.djvu:file (the link does not work!!). This should work: http://ncatlab.org/nlab/files/RobbinSalamonPhaseFunctionsPathIntegrals.djvu. I first tried to upload it on my personal nlab and it told me that it is 150 kb and that the limit is 100kb so I needed to do it in main nlab. Then I uploaded it first with error (few pages were missing) and replaced it by going back to the upload page and now the link here shows as if the file does not exist, but it does -- if you press on questionmark all is OK. On my page there is a doi to sequel paper of Robbin and Salamon.
@Zoran The second link worked for me. It required me to save and then djvu worked on that. (I only know their work on the Conley index. )
Several years on, what’s the retrospective view on this kantization idea? Did it all get taken up within motivic quantization?
I ask since following the development by Mike of an enriched homology over here, I was reminded of those old conversations on path integrals and groupoid cardinality/Leinster measure, as in Urs’s paper and then Johan Alm’s Quantization as a Kan extension.
I haven’t looked at this old stuff since then. One thing that we were after is a conceptualization of what is now well understood as the pull-push formula for quantization of Dijkgraaf-Witten theory. And yes, the motivic quantization idea generalizes this ways from the finite case.
But these old entries on Kantization should just be removed. To the extent that there is something worthwhile in them, it must have been superceded meanwhile.
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