BRST Extension of Geometric Quantization |
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Authors: | Ronald Fulp |
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Institution: | (1) Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA |
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Abstract: | 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. |
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Keywords: | geometric quantization BRST quantization |
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