Signal Transmission Along Singularity Free Gradient Fields and Quantization Caused by Internal Degrees of Freedom

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 F^a with a fibre-wise defined symplectic structure, a principal bundle P^a and a Heisenberg group bundle. For X = const. The geometry of P^a 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 F^a. This is related to signal transmission.