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Weyl-Wigner-Moyal formulation of a Dirac quantized constrained system
An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics
suitable for a Dirac quantized constrained system is proposed. In this
formulation, quantum observables are described by equivalent classes of Weyl
symbols. The Weyl product of these equivalent classes is defined. The new Moyal
bracket is shown to be compatible with the Dirac bracket for constrained
systems
Enumerations relating braid and commutation classes
We obtain an upper and lower bound for the number of reduced words for a
permutation in terms of the number of braid classes and the number of
commutation classes of the permutation. We classify the permutations that
achieve each of these bounds, and enumerate both cases.Comment: 19 page
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