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Prequantization

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

Abstract

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.

Keywords

Vector Field Line Bundle Commutation Relation Central Extension Curvature Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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