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  What restriction does BRST symmetry put on the Hamiltonian of a (lie group) gauge theory?

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As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following: "when QFT was reformulated in fiber bundle language for application to problems in the topology of low-dimensional manifolds, did it become apparent that the BRST 'transformation' is fundamentally geometric" I am aware of how ghosts are Maurer-Cartan form on the (infinite dimensional) group of gauge transfprmations of one's principle bundle... Now the above quote continues, "The relationship between gauge invariance and "BRST invariance" forces the choice of a Hamiltonian system whose states are composed of "particles" according to the rules familiar from the canonical quantization formalism. This esoteric consistency condition therefore comes quite close to explaining how quanta and fermions arise in physics to begin with."

Does anyone know what this second half of the quote is talking about? E.g. what "relationship", what "esoteric consistency condition, anr which special "form of Hamiltonian" is forced on which (presumably upon quantization) gives rise to particles ...? If the whole thing makes sense, does anyone know any references to this matter? (preferably, original sources...)
asked Apr 5, 2016 in Theoretical Physics by vandervoort (90 points) [ no revision ]
retagged Apr 5, 2016

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