Insights Introduction to Perturbative Quantum Field Theory - Comments

[Urs Schreiber]

Actually limits of traces (e.g. over denser and denser lattice discretizations), and these limits are infinite-dimensional (i.e., functional) integrals.

Not sure what you want me to say. I won't be considering explicit path integrals. Maybe you could point to some concrete article and say something like: "How would you phrase that construction in terms of diffeological spaces!"?

 

[A. Neumaier]

Not sure what you want me to say. I won't be considering explicit path integrals. Maybe you could point to some concrete article and say something like: "How would you phrase that construction in terms of diffeological spaces!"?

You refer to the path integral in Remarks 15.4 and 16.2 of
https://ncatlab.org/nlab/show/geometry+of+physics+--+A+first+idea+of+quantum+field+theory
So these are considered only as loose heuristics, not with a diffeological interpretation?

 

[Urs Schreiber]

You refer to the path integral in Remarks 15.4 and 16.2 of
https://ncatlab.org/nlab/show/geometry+of+physics+--+A+first+idea+of+quantum+field+theory
So these are considered only as loose heuristics, not with a diffeological interpretation?

Absolutely. I don't consider explicit path integrals. These remarks are meant for the reader who will have been exposed to the usual informal path integral lore and are meant to explain how the axiomatic construction of the S-matrix and of the interacting observables in causal perturbation theory correspond to that informal lore.

I'll try to rephrase these remarks a little to make sure that this becomes clear.

 

[Urs Schreiber]

I'll try to rephrase these remarks a little to make sure that this becomes clear.

Okay, I have touched the wording of these two remarks:

• Intuitive interpretation of the perturbative S-matrix as a "path integral"
• Intuitive interpretation of Bogoliubov's formula in terms of a "path integral"

 

[A. Neumaier]

Okay, I have touched the wording of these two remarks:

• Intuitive interpretation of the perturbative S-matrix as a "path integral"
• Intuitive interpretation of Bogoliubov's formula in terms of a "path integral"

misprint: simimlarly

 

[Leo1233783]

With Greg we are looking for a solution now. A technically simple solution would be to simply include that webpage inside an "iframe" within the PF-Insights article. But maybe this won't be well received with the readership here? If anyone with experience in such matters has a suggestion, please let me know.

Did you found a solution ? if not, I can try. What or where are exactly a typical input and a typical output ?

 

[Urs Schreiber]

Did you find a solution ?

No, I didn't.

if not, I can try.

That would be great!

What or where are exactly a typical input and a typical output ?

Okay, my input source is here .

The output format that is needed for PF-Insights is mainly standard HTML, except for the maths formulas.

For the maths formulas

1. single dollar sign delimiters in my source need to be turned into double hash delimiters
2. backslash followed by "hookrightarrow" in my source needs to be turned into plain "rightarrow" (because the hookrightarrows come out as strange graphics otherwise - alternatively if you know how to generate a decent hookrightarrow here, that would be welcome).

For the text decoration:

1. underscore delimiter needs to be turned into the HTLML "em"-tag environment
2. star delimiter needs to be turned into the HTML "strong"-tag environment

For the hyperlinks:

1. In my source a string "some text" inside double square brackets wants to become a hyperlink to "https://ncatlab.org/nlab/show/some+text".
   
2. Alternatively I have single square brackets around "some text" followed by "page#anchor" in round brackets, and this wants to be turned into "some text" equipped with a hyperlink to "https://ncatlab.org/nlab/show/page#anchor".

Other markup I use could just be stripped off. For instance

1. I use environments for automatically numbered Definitions/Propositions/Proofs. Of course it would be great to automatically turn them into something saying "Definition" or "Proposition" etc. but to first approximation just discarding that environment code would work.
2. Similarly I have a handful of tables in the code, in some probably self-explanatory encoding. In principle these could be turned into HTML-tables, but to first approximation we could just discard them.

Please let me know if this is information that you can use. Otherwise I'll be happy to try to say more.

Thanks again for looking into this!

 

[Leo1233783]

Data received. A simple line transformer will be probably enough and extensible. Else I have other solutions. I'll come back to you in a private message :)

 

[Urs Schreiber]

To everyone:

The terrific Leo1233783 above (who seems to like to remain anonymous) has now provided tremendous help with converting my source to PF-Insights format. A million thanks for that!

This way we are finally set for the series on QFT to begin:

A First Idea of Quantum Field Theory – 20 Part Series

So far that page has just a few lead-in words and then a table of contents. In the next days and weeks, each chapter in that table of contents will appear as a separate PF-Insights article, and will be hyperlinked from that page.