• Jȩdrzej Śniatycki
Part of the Applied Mathematical Sciences book series (AMS, volume 30)


The aim of this chapter is to construct a linear monomorphism from the Poisson algebra of (X, ω) to the space of linear operators on an appropriate Hilbert space, associating to each function f on X a linear operator Pf so that the commutation relations are satisfied for each pair of functions f and g on X. It should be noted that the mapping f ↦ (ħ/i)ξf satisfies (3.1) but it fails to be a monomorphism since its kernel consists of the space of all constant functions on X. Thus, we need a central extension of the Lie algebra of Hamiltonian vector fields on X by the additive group R of real numbers.


Vector Field Line Bundle Commutation Relation Central Extension Curvature Form 
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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Jȩdrzej Śniatycki
    • 1
  1. 1.The University of CalgaryCalgaryCanada

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