General vector field representations of local Heisenberg systems

  • F. B. Pasemann
1. Quantization Methods and Special Quantum Systems
Part of the Lecture Notes in Physics book series (LNP, volume 139)


A quantization procedure is proposed starting with the Lie algebra \(\mathbb{G}\) of infinitesimal symmetries of a system and a \(\mathbb{G}\)-action on a principle bundle
. For quasi-complete \(\mathbb{G}\)-actions the constructed vector field operators are essentially skew adjoint and can be interpreted as canonical momentum observables of a local Heisenberg system. Integrability of general vector field representations of local Heisenberg systems to unitary representations of corresponding Heisenberg systems is discussed.


Vector Field Unitary Representation Volume Form Principal Bundle Base Manifold 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • F. B. Pasemann
    • 1
  1. 1.Institut für Theoretische PhysikClausthalGermany

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