Heisenberg groups—A unifying structure of signal theory, holography and quantum information theory |
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Authors: | Ernst Binz Sonja Pods Walter Schempp |
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Affiliation: | 1. Lehrstuhl für Mathematik I, Universit?t Mannheim, D-68131, Mannheim, Germany
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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. |
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