Communications in Mathematical Physics

, Volume 136, Issue 2, pp 209–229 | Cite as

Geometric BRST quantization, I: Prequantization

  • José M. Figueroa-O'Farrill
  • Takashi Kimura
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Line Bundle 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • José M. Figueroa-O'Farrill
    • 1
  • Takashi Kimura
    • 2
  1. 1.Instituut voor Theoretische FysicaUniversiteit LeuvenHeverleeBelgium
  2. 2.Department of Mathematics61200 University of TexasAustinUSA

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