Abstract
A complete canonical formulation of the BRST theory of systems with redundant gauge symmetries is presented. These systems includep-form gauge fields, the superparticle, and the superstring. We first define the Koszul-Tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic. The global existence of the BRST generator is then demonstrated, and the BRST charge is proved to be unique up to canonical transformations in the extended phase space, which includes the ghosts. Finally, the BRST cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits, as in the irreducible case. This is done by re-expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree, which are identified with the ghosts of ghosts. The quantum cohomology is not dealt with.
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Communicated by L. Alvarez-Gaumé
Aspirant du Fonds National de la Recherche Scientifique (Belgium)
Chercheur qualifié au Fonds National de la Recherche Scientifique (Belgium)
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Fisch, J., Henneaux, M., Stasheff, J. et al. Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts. Commun.Math. Phys. 120, 379–407 (1989). https://doi.org/10.1007/BF01225504
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DOI: https://doi.org/10.1007/BF01225504