A First Idea of Quantum Field Theory - 20 Part Series - Comments

[Urs Schreiber]

Greg Bernhardt submitted a new PF Insights post

A First Idea of Quantum Field Theory - 20 Part Series

Continue reading the Original PF Insights Post.

 

[BvU]

I see 66 links between 'This series' and 'Acknowledgement'. Wouldn't just one link have been enough ?

(By the way, an awful lot of them don't work ! )

 

[Urs Schreiber]

an awful lot of them don't work !

Those links not activated yet are pointing to articles that appear further down in the series. They will become active incrementally as the series progresses.

Wouldn't just one link have been enough ?

Here I am not sure what you have in mind. But the links are just an offer, leading to further information, not a request to click on them. If you feel like not following any, that's fine.

 

[Greg Bernhardt]

(By the way, an awful lot of them don't work ! )

The keywords go to ncatlab for more information. The chapter links aren't active yet because they haven't been released, but once they are they will be active. Hold tight, first chapter releases tomorrow! :)

 

[A. Neumaier]

The links to expl. 8.16 and 10.16 (and perhaps others) do not work!

 

[Urs Schreiber]

The links to expl. 8.16 and 10.16 (and perhaps others) do not work!

Thanks for the alert! Indeed, all PF-internal links had been broken since my last update. Not sure why this happened. But I have fixed it now. (Or so I think.)

 

[Urs Schreiber]

Following public request, I have compiled a stand-alone list of references, see above under References.

But notice that detailed pointers to the literature are included in each chapter, alongside the text, attached to the relevant definitions or propositions.

 

[Duong]

Hello,

I believe you once said there are results that are proved only by doing QFT rigorously. Could you please name some of such results and if possible point me to the explicit sources of those results? Thanks in advance.

 

[Urs Schreiber]

I believe you once said there are results that are proved only by doing QFT rigorously.

Just to nitpick, I'll say that every proof is necessarily rigorous, otherwise it is not a proof but a plausibility argument that may still fail upon examination.

Could you please name some of such results and if possible point me to the explicit sources of those results?

A list of theorems in QFT, with further pointers is at

Algebraic Quantum Field theory -- Contents --> Theorems

The main one that we proved in the series (Prop. 16.19) is the main theorem of perturbative renormalization. This implies the theorem that renormalization via UV-regularization exists (Prop. 16.23).

Then there is a list of famous structural theorems that are proven from the Haag-Kastler axioms (which we derived in Prop. 15.30). The Reeh-Schlieder theorem (recently picked up by Witten, see section 2 of arXiv:1803.04993), the Osterwalder-Schrader theorem ("Wick rotation exists"), the PCT theorem and, last not least, the spin-statistics theorem. The classical reference here is this textbook:

• R. F. Streater and A. S. Wightman,
  "PCT, Spin and Statistics, and All That",
  Princeton University Press

 

[Urs Schreiber]

Michael Duetsch's textbook on Mathematical Quantum Field Theory is finally out:

nLab entry, publisher page .

It refers to PF Insights, notably for the proof of renormalization via counterterms (theorem 3.4.9 in the book, referring to PF Insights, Chapter 16)