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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.
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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
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has generated this notice as a focus of cleanup efforts, and also contacted several contributing editors of the article to bring their attention to the problem. You should use this section to discuss possible resolution of the problem and achieve consensus for action. Only when there is a consensus
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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
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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
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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.
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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.
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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.
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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.
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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.
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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.
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that the article is now cleaned up should you then de-list it by deleting the cleanup tag from the article, this causes the article to drop off the monthly cleanup-needed list page.
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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.--
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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.
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to talk about the relationship between the BRST operator and the "covariant exterior derivative" on a local section of the gauge bundle.
55:. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please see
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It would be great to know which authors are meant, when a few years later was, and what is meant by the rigorous alternative.
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there are developments on techniques based on Koszul complexes as a resolution of the (structure ring of the) phase space
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Please check that everything is in order, I'm not at all confident in this field. —
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This is saying that BRST is a rigorous alternative to path integrals (
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What is the relevance of the Koszul complex to this article ?
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