Abstract
The equivalence of Dirac quantization and intrinsic quantization for arbitrary observables not preserving the vertical polarization is examined for systems with first class constraints that may be considered as the vanishing of the momentum map to a lifted group action. Using a generalized Weyl ordering prescription applicable to arbitrary cotangent bundles we derive necessary and sufficient conditions for the equivalence of the two approaches for different classes of functions. A strong obstruction is found if one requires equivalence for all invariant functions, essentially only admitting trivial bundles. By a restriction to an adequate class of “strongly admissible functions”, equivalence can always be obtained in the case of a free group action. Implications for the case of non-free actions and the dependence on the particular quantization scheme are discussed.
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Communicated by H. Araki
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Emmrich, C. Equivalence of extrinsic and intrinsic quantization for observables not preserving the vertical polarization. Commun.Math. Phys. 151, 515–530 (1993). https://doi.org/10.1007/BF02097025
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DOI: https://doi.org/10.1007/BF02097025