Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also BRST operators for many systems require regularization to be well-defined. In our more restricted context, we show that our treatment does not suffer from any of these difficulties.
Similar content being viewed by others
References
Woodhouse N.M.J. (1992) Geometric Quantization. Oxford Univ. Press, Oxford
Henneaux M., Teitelboim C. (1992) Quantization of Gauge Systems. Princeton University Press, New Jersey
Rogers A. (1980) “A global theory of supermanifolds”. J. Math. Phys. 21: 1352
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fulp, R. BRST Extension of Geometric Quantization. Found Phys 37, 103–124 (2007). https://doi.org/10.1007/s10701-006-9090-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-006-9090-8