Dispersion dynamics applications

One starting point is the Klein Gordon equation and the stable wave packet [1]. Simpler is relativity: insert Planck’s law and the de Broglie hypothesis. In simple units, angular frequency = +(k²+m_o²)^1/2, with m_o the rest mass. Now differentiate with respect to wave vector k. Three related velocities are the phase velocity, the group velocity and the speed of light. Dispersion dynamics requires consistently, negative mass in the antiparticle, with negative kinetic energy, negative momentum and negative angular velocity. These properties have widespread application in: the Hall effect; superconductivity; the switching principle; galactic rotational velocities; event horizons, uncertainty, intrinsic spin, etc.
[1] Dispersion dynamics in the Hall effect and pair bonds in HiTc, Bourdillon AJ, Nova Science, 1917, ISBN 978-1-53612-568-9