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Signal Transmission Along Singularity Free Gradient Fields and Quantization Caused by Internal Degrees of Freedom
p. 105-120
Abstract
Any singularity free vector field X defined on an open set in a three-dimensional Euclidean space with curl X = 0 admits a complex line bundle Fa with a fibre-wise defined symplectic structure, a principal bundle Pa and a Heisenberg group bundle. For X = const. The geometry of Pa defines the Schrödinger representation of any fibre of the Heisenberg group bundle and a quantization procedure for homogeneous quadratic polynomials on the real line visualised as a transport along field lines of internal degrees of freedom in Fa. This is related to signal transmission.
Index
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References
Bibliographical reference
Ernst Binz and Walter Schempp, « Signal Transmission Along Singularity Free Gradient Fields and Quantization Caused by Internal Degrees of Freedom », CASYS, 10 | 2001, 105-120.
Electronic reference
Ernst Binz and Walter Schempp, « Signal Transmission Along Singularity Free Gradient Fields and Quantization Caused by Internal Degrees of Freedom », CASYS [Online], 10 | 2001, Online since 07 October 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=1113
Authors
Ernst Binz
Lehrstuhl für Mathematik I, Universität Mannheim, D-68131 Mannheim, Germany
Walter Schempp
Lehrstuhl für Mathematik I, Universität Siegen, D-57068 Siegen, Germany