Natural Microstructures Associated with Singularity Free Gradient Fields in Three-space and Quantization
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چکیده
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 Ga . For the non-vanishing constant vector field X the geometry of Pa defines for each frequency a Schrödinger representation of any fibre of the Heisenberg group bundle and in turn a quantization procedure for homogeneous quadratic polynomials on the real line.
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تاریخ انتشار 2000