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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 23rd 2015

I have started a category:reference page

such as to be able to point to it for reference, e.g. from Kontsevich 15 etc.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 28th 2018

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 28th 2018

It says there about dcct and other articles:

Observe that these references also deal with variants of shifted pre-symplectic structures on stacks, but the non-degeneracy condition is almost never satisfied as everything takes place in the realm of underived stacks.

I was reminded of our conversation here.

By the way, the talk slides link at Prequantum field theories from Shifted symplectic structures doesn’t work.

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 28th 2018
• (edited Mar 1st 2018)

Good final flourish to the paper!

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 1st 2018
• (edited Mar 2nd 2018)

It says there about dcct and other articles:

Observe that these references also deal with variants of shifted pre-symplectic structures on stacks, but the non-degeneracy condition is almost never satisfied as everything takes place in the realm of underived stacks.

It is noteworthy that non-degenerate symplectic structure in gauge field theory is all about recitifying a homotopy-theoretic structure: the gauge-fixing of the BV-BRST complex which ensures the non-degenerate graded symplectic structure is a means to quantize homotopy-theoretically by doing it naively but degreewise, respecting a differential (chapter 11). This is in direct analogy to how a naive Lie algebra considered degreewise and respecting a differential (hence a dg-Lie algebra) is a rigidified model for a strong homotopy Lie algebra.

While it is true that presently this homotopy-rigidified trick is the only known way to quantize gauge field theory, in general, it is clear from the point of view of homotopy theory that this must be but a tool and a convenience, not a fundamental necessity. It ought to be true that there is a homotpy-quantization procedure which reads in the non-gauge fixed and hence degenerate presymplectic current (aka shifted pre-symplectic structure) and quantizes it right away.

This is ultimately what Marco Benini and Alexander Schenkel are headed for in their homotopical AQFT. Their toy example of free electromagnetism sort of works this way already, but there is a long way to go until this will be understood generally. Meanwhile, it is good to have a clear picture of the role that symplectic rather than pre-symplectic structure plays in QFT.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeMar 1st 2018

So a way needs to be found to realise

quantization is the result of forming the homotopy quotient of the space of Lagrangian data by these duality relations?

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMar 2nd 2018
• (edited Mar 2nd 2018)

That sounds possibly circular, since how would one know about duality relations without first having an independent construction of quantization in the first place. But who knows what the future will bring.

But the point under discussion above is a different one: The Lagrangian densities that define Lagrangian field theory (up to renormalization choices) a priori yield higher pre-symplectic structure, not higher symplectic structure. The latter is obtained only after auxiliary fields are adjoined and a choice of BV-gauge fixing is made, which is directly analogous to choosing a differential graded algebra over an operad as a rectified model for an $\infty$-algebra over an $\infty$ -operad. It works and is often convenient, sometimes it may even be the only tool under control, but it is not part of the definition of the homotopy theoretic concept.

That’s why I always thought it pays to have a thorough look at higher pre-quantum geometry first, before hastening to make assumptions about what higher quantum geometry should be like. First things first. In any case, it is not a fault or omission of higher pre-quantum geometry not to feature derived geometry and non-degenerate shifted symplectic form, rather this is the nature of the subject of Lagrangian field theory. Or so I think.

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeMar 2nd 2018

And the extension to look at differential graded algebroids belongs to same approach? I see from this abstract that your former student is developing this:

we explain how to apply this machinery to the case of non-split formal moduli problems under a given derived affine scheme; this situation has been dealt with recently by Joost Nuiten, and requires to replace differential graded Lie algebras with differential graded Lie algebroids.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMar 2nd 2018
• (edited Mar 2nd 2018)

Now by “the same approach” you are referring to the general topic of rectification, right? Yes, the concept of dg-Lie algebroids is (or should be) the rectification of the concept of general $\infty$-Lie algebroids. To be more precise I would have called Joost’s def 2.1 in arXiv:1712.03442 that of dg-Lie-Rinehart pairs, but of course the difference is negligible in a context of dg-geometry.

• CommentRowNumber10.
• CommentAuthorTim_Porter
• CommentTimeJan 2nd 2019
• (edited Jan 2nd 2019)

Removed the double indexation and added a link to a draft version of my chapter for New Spaces in Mathematics and Physics.

• CommentRowNumber11.
• CommentAuthorGuest
• CommentTimeApr 17th 2019
I can't see anything here about electromagnetic geometry.

John Duffield
• CommentRowNumber12.
• CommentAuthorDavid_Corfield
• CommentTimeMay 3rd 2019

• CommentRowNumber13.
• CommentAuthorDavid_Corfield
• CommentTimeMay 3rd 2019

The book doesn’t quite match up with the conference, and so I’ve separated them. At some point should link the entries, but no time now.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeFeb 8th 2020

One of the editors just wrote in asking me to promotly remove several names, apparently their contributions were cancelled.

• CommentRowNumber15.
• CommentAuthorTim_Porter
• CommentTimeNov 24th 2020
• (edited Nov 24th 2020)

I changed the projected publication date to 2021!

• CommentRowNumber16.
• CommentAuthorDavid_Corfield
• CommentTimeMar 6th 2021

Looks like these volumes are about to appear, so I added in CUP websites for them.

• CommentRowNumber17.
• CommentAuthorzskoda
• CommentTimeMar 7th 2021
• (edited Mar 7th 2021)

Somehow a part of the books can be seen on googlebooks already (some of the individual pages) with issue date of March 31. For example, Kontsevich’s contribution has 4-5 pages more than the version previously circulating among colleagues.

• New spaces in mathematics: formal and conceptual reflections gBooks, New spaces in physics: formal and conceptual reflections gBooks

P.S. I reinstalled ubuntu (now 20.04) on my main machine and still adjusting parameters, if you notice any strange behaviour from my posts anywhere around, please let me know.

• CommentRowNumber18.
• CommentAuthorJohn Baez
• CommentTimeMar 23rd 2021

#### What experiments tell us about space and time (John Baez)

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeMar 23rd 2021
• (edited Mar 23rd 2021)

removed the duplication of the book title and URL

and reformatted slightly to better fit the usual pattern

(Incidentally, I am learning about this finally being published now only through the news. It’s been a long time, over 5 years since submission of the contributions.)

• CommentRowNumber20.
• CommentAuthorUrs
• CommentTimeMar 23rd 2021
• (edited Mar 23rd 2021)

The GoogleBooks link took me to a Croatian dialogue box. So I have replaced .hr with .us, just so that if the dialogue box comes up, more people know what to make of it.

• CommentRowNumber21.
• CommentAuthorUrs
• CommentTimeMar 23rd 2021

Oh, somebody give me a sanity check:

On top of p. v it says

Contents

Contents for New Spaces in Physics $\;\;\;\;$ page vii

Introduction $\;\;\;\;$ page 1

Introduction $\;\;\;\;$ page 1

followed by what clearly must be the content of “New Spaces in Mathematics”;

while the top of p. vii is says both

Contents for New Spaces in Physics

Contents for New Spaces in Mathematics $\;\;\;\;$ page vii

followed by what must be the content of “New Spaces in Physics”;

$\,$

There seem to be a couple of problems here.

(Am I missing something? I am looking at the GoogleBooks-version. Couldn’t get access via my NYU account, strangely.)

• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeMar 23rd 2021

I have fixed the missing line-breaks in the list of book chapters.

While I was at it I turned them into subsections, too. Then I started adding author links and arxiv links to the book chapters.

Not complete yet, but I am running out if steam niw.

• CommentRowNumber23.
• CommentAuthorUrs
• CommentTimeMar 23rd 2021

have now added author links and hyperlinked keywords to essentially all book chapters, and arXiv pointers for the (few) cases where I new about them (haven’t searched much yet, please add pointers where available)

• CommentRowNumber24.
• CommentAuthorUlrik
• CommentTimeMar 23rd 2021

Add links to preprints for the chapters by Anders Kock and Timothy Porter.

• CommentRowNumber25.
• CommentAuthorUrs
• CommentTimeMay 20th 2021

Just got an email that now the book is officially/actually published.

Checking on GoogleBooks whether the glitches pointed out in #21 have been fixed… Hm: partially.