Mathematical Quantum Field Theory - Phase Space - Comments

[Urs Schreiber]

Greg Bernhardt submitted a new PF Insights post

Mathematical Quantum Field Theory - Phase Space

Continue reading the Original PF Insights Post.

 

[Urs Schreiber]

There was a mix up in the order of the introductory paragraphs. Should be fixed now.

 

[Urs Schreiber]

I should maybe point that the Peierls bracket derived in chapter 8. Phase space (theorem 8.7), which is the covariant Poisson bracket on the covariant phase space, is the basis of what is called the "global approach to QFT" in the traditional-style textbook:

• Bryce DeWitt, The global approach to Quantum Field Theory (2 volumes), Oxford 2003

 

[A. Neumaier]

I should maybe point that the Peierls bracket derived in chapter 8. Phase space (theorem 8.7), which is the covariant Poisson bracket on the covariant phase space, is the basis of what is called the "global approach to QFT" in the traditional-style textbook:

• Bryce DeWitt, The global approach to Quantum Field Theory (2 volumes), Oxford 2003

Yes, maybe in an introductory section. It would be good if each of the articles in the sequence would begin with an initial section summarizing what is to follow, what it means in terms of buzzwords (to be explained later), and giving basic sources for further reading.

 

[Urs Schreiber]

It would be good if each of the articles in the sequence would begin with an initial section summarizing what is to follow,

That seems to be just what I have been doing. Is it not working?

Regarding sources: I have citations in the text. I wish there would be a general source I could cite, but maybe it doesn't exist. In the case at hand, while DeWitt's books advertizes the Peierls bracket, I hesitate to recommend using it. The source which I do cite extensively, which is Khavkine 14, seems the best source for the result, and I tried to provide all the required context and lead-in to highlight its conceptual role.

 

[A. Neumaier]

That seems to be just what I have been doing. Is it not working?

Indeed, for the whole articles, you have it - but in too overwhelming detail. I'd prefer if the chapter introductions are more elementary and less detailed, and if the overview over the details are delegated to the top of each section. (I wrote the comment since the section ''Covariant phase space'' started without introduction, and I had mistakenly taken it for the start of the whole chapter.) And if possible the same again on a subsection level.

In the present chapter ''Phase space'', the chapter summary might start with

In this section we discuss these topics:

• Covariant phase space
• BV-Resolution of the covariant phase space
• Hamiltonian local observables

and then relate in the most elementary way why these items are relevant and what purpose they have in the grand scheme of things. Then each section should have its own, a (only slightly) more technical introduction, perhaps at the level of the present global introduction, ideally even more softened. All introductions should be written in the most inviting way, drawing attention to possible prior knowledge on the side of the reader but not demanding more than absolutely necessary to get the picture. In this way even those who cannot digest the details (or at least not in one go) will benefit from browsing the articles in a more lightly way, and multiple readings allow one to go deeper in each iteration.

In the case at hand, while DeWitt's books advertizes the Peierls bracket, I hesitate to recommend using it. The source which I do cite extensively, which is Khavkine 14, seems the best source for the result, and I tried to provide all the required context and lead-in to highlight its conceptual role.

Putting this somewhere at the top of the section ''Covariant phase space'' would be a way of satisfying both you and me.

 

[A. Neumaier]

- ''discuss of Gauge fixing'' should be discussion
- "In def. 7.30 we regard" has a spurious line break
-"\gt maybe better consider formal power series" - unresolved html symbol

 

[Urs Schreiber]

- ''discuss of Gauge fixing'' should be discussion
- "In def. 7.30 we regard" has a spurious line break
-"\gt maybe better consider formal power series" - unresolved html symbol

Thanks! Fixed now.