Heisenberg groups: a unifying structure of signal theory, holography and quantum information theory

  • Authors:

  • Ernst Binz;Sonja Pods;Walter Schempp

  • Affiliations:

  • Lehrstuhl für Mathematik I, Universität Mannheim, Mannheim, Germany;Lehrstuhl für Mathematik I, Universität Mannheim, Mannheim, Germany;Lehrstuhl für Mathematik I, Universität Siegen, Siegen, Germany

  • Venue:
  • The Korean Journal of Computational & Applied Mathematics
  • Year:
  • 2003

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Abstract

Vector fields in three-space admit bundles of internal variables such as a Heisenberg algebra bundle. Information transmission along field lines of vector fields is described by a wave linked to the Schrödinger representation in the realm of time-frequency analysis. The preservation of local information causes geometric optics and a quantization scheme. A natural circle bundle models quantum information visualized by holographic methods. Features of this setting are applied to magnetic resonance imaging.