Geometric BRST quantization,I: Prequantization |
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Authors: | José M Figueroa-O'Farrill Takashi Kimura |
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Institution: | (1) Instituut voor Theoretische Fysica, Universiteit Leuven, Celestijnenlaan 200D, B-3001 Heverlee, Belgium;(2) Department of Mathematics, 61200 University of Texas, 78712 Austin, Texas, USA |
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Abstract: | This is the first part of a two-part paper dedicated to the definition of BRST quantization in the framework of geometric quantization. After recognizing prequantization as a manifestation of the Poisson module structure of the sections of the prequantum line bundle, we define BRST prequantization and show that it is the homological analog of the symplectic reduction of prequantum data. We define a prequantum BRST cohomology theory and interpret it in terms of geometric objects. We then show that all Poisson structures correspond under homological reduction. This allows to prove, in the BRST context, that prequantization and reduction commute. |
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