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Differential Geometric Methods in Mathematical Physics pp 38–48Cite as

General vector field representations of local Heisenberg systems

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

Abstract

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.

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Authors and Affiliations

  1. Institut für Theoretische Physik, TU Clausthal, 3392, Clausthal, Germany

    F. B. Pasemann

Authors
  1. F. B. Pasemann
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Heinz-Dietrich Doebner

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© 1981 Springer-Verlag

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Pasemann, F.B. (1981). General vector field representations of local Heisenberg systems. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_21

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  • DOI: https://doi.org/10.1007/3-540-10578-6_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10578-7

  • Online ISBN: 978-3-540-38573-8

  • eBook Packages: Springer Book Archive

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