Talk:BRST quantization

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While I have learnt BRST methods elsewhere, this article presents it from a novel viewpoint that I am not familiar with. Unfortunately, it is also vague and confusing enough that I can't quite grasp what the author means.

It's still very much in draft, and I anticipate that once it is a bit more complete (I have more transcribing to do) I will edit it down drastically. In the meantime, specific suggestions are very much welcome. Michael K. Edwards 23:22, 3 September 2006 (UTC)

Also, I have no intention of presenting a "novel viewpoint". It is true that first-year QFT textbooks, even good ones, tend to do a poor job of articulating the significance of the BRST formalism. But it seems that most active researchers on both the mathematical and physical sides of the fence have been aware of the importance of BRST cohomology in gauge theories since at least the late 80's. There are several perspectives from which a "vanilla" encyclopedia article could be written, and the geometrical perspective which I prefer may not be the most current at the moment; but I don't think there's anything controversial or original about the main line of my exposition. (Verbose yes; controversial no.) And I have so far resisted the temptation to load the dice by using the elegant but unconventional language of the Frölicher-Nijenhuis calculus to talk about the relationship between the BRST operator and the "covariant exterior derivative" on a local section of the gauge bundle. Michael K. Edwards 05:09, 4 September 2006 (UTC)

Merging the article with BRST formalism. I think we should merge the two article and rewrite/edit the two in a more coherent point of view. I am willing to help improving the article, but I am going to wait until the two get merged or whether someone gives a good reason why we should have two articles on BRST. Hwasungmars (talk) 10:29, 6 March 2008 (UTC)

Mathematical section. I added a section about mathematical formulation of BRST and removed any reference to the Ward operator that I felt was not used in the same context here as in the published literature. I am not a physicist, so I did not touch the rest of the article. Getmko Getmko (talk) 16:24, 19 November 2009 (UTC)

Merged from BRST formalism

Following Wikipedia:Articles for deletion/BRST formalism consensus was to merge that article in here. I've cut and pasted the content into the BRST quantization#BRST formalism, but I suspect that there is much duplication. Alas I don't know enough on the subject to do more than that so I hope subject experts can clean it up a bit.--Salix (talk): 14:03, 3 November 2010 (UTC)

This has been done a long time ago now, but I think it is a terrible idea to just throw together different articles without any attempt to harmonize their content.--93.220.219.65 (talk) 23:12, 2 December 2011 (UTC)

I just got done harmonizing this. Yes, 14 years later. So it goes. Time had taken its toll, and the article was a train-wreck; I straightened out everything as best I could, in a proper workman-like fashion. 67.198.37.16 (talk) 02:50, 28 May 2024 (UTC)

I disambigued stuff

Please check that everything is in order, I'm not at all confident in this field. — Kallikanzarid^talk 11:13, 19 December 2010 (UTC)

What is the relevance of the Koszul complex to this article ?

In the section BRST quantization#Mathematical approach to BRST there are developments on techniques based on Koszul complexes as a resolution of the (structure ring of the) phase space $M$ or of the fiber $M_{0}$ of a moment map. Koszul complexes are very interesting and useful mathematical objects, but there is no explanation of their relevance to BRST quantization. Most of the references make no reference to Koszul complexes, i guess that the Kostant-Sternberg article is the one introducing Koszul into BRST, because of its title, but to me the connection is far from obvious. How would the BRST charge relate to a differential of a Koszul complex ? I suppose the "Q-complex" is derived from the Koszul resolution described in the article whence one defines a "Chevalley-Eilenberg complex" whose total complex perhaps has (something close to) a BRST charge as differential; but there is not even a mention of ghosts so it is difficult to work out as a newcomer. Anyone feeling like adding some clarifications to that section -i do not mean at all to have it removed, it is certainly interesting once one understands it. Thank you. Plm203 (talk) 12:12, 14 August 2023 (UTC)

That section was recently added, and is problematic in a large number of ways. It needs a major cleanup. 67.198.37.16 (talk) 20:54, 27 May 2024 (UTC)

Which other authors

The article states:

Work by other authors a few years later related the BRST operator to the existence of a rigorous alternative to path integrals when quantizing a gauge theory.

It would be great to know which authors are meant, when a few years later was, and what is meant by the rigorous alternative.

Logicdavid (talk) 22:59, 14 February 2024 (UTC)

This is saying that BRST is a rigorous alternative to path integrals (i.e. to the pre-BRST approach to quantizing using path integrals). A "few years" is literally 2-4 years. Stuff happens fast. Who did most of the heavy lifting? I dunno. What were the seminal papers? Good question. 67.198.37.16 (talk) 20:59, 27 May 2024 (UTC)