Talk:Conformal bootstrap

= Fields =

Current version (as edited by 67.198.37.16 - can't you create a nickname?) contains a mention of "(field) operators". To my knowledge, this terminology is not used in the contemporary literature on conformal field theories. 67.198.37.16, can you please provide some references to textbooks talking about "field operators"? Also "of course" in the sentence afterwards does not sound encyclopedic. — Preceding unsigned comment added by PhysicsAboveAll (talk • contribs) 15:34, 17 September 2015 (UTC)


 * Hi PhysicsAboveAll,


 * First, some basic requests: can you place comments at the bottom of a talk page, instead of the top? That way, they are in chronological order. That's the WP convention. Its great if you can also add a subject heading, too. You can do both at the same time by clicking on the "new comment" tag.


 * You can sign your posts by using 4 tildes in a row, like so: ~ that automatically adds your name and a date to your posts.


 * I'm used to calling them fields, because maybe I'm older than you, and when I grew up, that is what they were called. I find it weird and confusing to call them operators; yes, of course, they are operators, but that is not all they are; they're more than that. But whatever, that is quibbling. If present-day literature calls them operators, then whatever, I guess its reasonable to call them that. But they still are fields, even if you call them something else :-)  Well, I guess maybe the confusion is this: does modern day literature call currents operators "currents", or are those called operators, without the word "current" playing a role? Charge operators? Or is the idea that they're all lumped into one?


 * Textbook references: try Bjorken and Drell. Landau and Lifshitz. JC Taylor. Itzykson and Zuber. The usage predates CFT by decades.


 * Of course, you can change the wording. Clarity and accuracy are important. 67.198.37.16 (talk) 22:43, 17 September 2015 (UTC)

Hi 67.198.37.16,

what you call "field operators" we now call "local operators". Conserved currents are examples of local operators. Some nonlocal operators can be expressed as integrals of local ops, e.g. charges are integrals of conserved currents. Of course there are tons of other nonlocal operators, like Wilson lines, defects and what not.

Calling local operators "fields" is discouraged in modern usage because that use would seem to assume implicit existence of some sort of Lagrangian or path integral descriptions where some of these "fields" would appear. But some known CFTs don't seem to allow any Lagrangian description, like the (2,0) theory in 6d. Other CFTs do allow Lagrangian description, but the local operators at the IR fixed point are not always trivially related to fields appearing in the Lagrangian. So even in these cases it's best to forget about the microscopic field origin of the operators and just call them local operators.

Textbooks you cite focus on perturbative QFT where local operators are built out of products fields so this distinction is less important.

I adjusted the text to fit the more modern usage. Hope you don't mind. PhysicsAboveAll (talk) 14:06, 18 September 2015 (UTC)


 * Yes, quite right; I don't mind at all. You've exposed a hole in how I think about things. 67.198.37.16 (talk) 17:10, 19 September 2015 (UTC)
 * Sorry about the numerical addr; I stay anonymous cause of the oft-combative nature of discussions on WP. The people in positions of power at WP have fragile egos and not the finest of intellects, which has decimated science authorship and participation. Oh well. By contrast, articles at this level of abstraction don't suffer such abuse; air's too rarified. Much more pleasant. 67.198.37.16 (talk) 17:31, 19 September 2015 (UTC)

= Renaming this page? = History of the conformal bootstrap may be a better title given the current contents. Sylvain Ribault (talk) 20:49, 20 October 2019 (UTC)

This article contains some technical content, some historical content, and references to the current status of the field. Conformal bootstrap is the inclusive title which covers all these aspects. PhysicsAboveAll (talk) 16:38, 9 November 2019 (UTC)