brst tablet - GADGET
Note that the BRST symmetry acts on a very different space than the gauge symmetry - the BRST symmetry acts on the extended phase space with ghosts (and ghosts-of-ghosts, etc.) and only BRST-invariant quantites are physically meaningful, while the original gauge symmetry (with potentially multiple parameters) acts on the original phase space. WHY BRST formulation works: Conditions imposed on QFT to find (how many ... BRST quantization (and BRST symmetry in general), at least in this point in my understanding of them, seem rather arbitrary and slightly miraculous.
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However, the cohomological nature of the BRST ch... The quote "esoteric consistency condition" undoubtedly refers to the fact that the BRST transformation is nilpotent (=squares to zero), which encodes a (possibly infinite) tower of consistency relations. The quote "comes quite close to explaining how quanta and fermions arise in physics to begin with" refers to the fact that physical states are counted/classified by BRST cohomology, and that ... quantum field theory - What is the relationship between BRST symmetry ...
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Am I being naïve? How can you prove that BRST theory is really equivalent to Gupta-Bleuler when the algebra is abelian? 1: See e.g. the last page on Timo Weigand's notes, or some remarks in the Scholarpedia article Becchi-Rouet-Stora-Tyutin symmetry (ctrl+f "gupta"). I am studying about BRST symmetry from the book of P&S (Peskin's and Schroeder's "An Introduction to QFT", Chapter 16.4).
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The authors construct a nilpotent charge operator and then they describe how it acts on single particle states. TL;DR: The BRST transformation rules for the ghost fields follow from requiring that the BRST/Slavnov operator squares to zero (= is nilpotent in physics jargon).