Pointparticle Systems on the Prototypes of Zeeman Manifolds and Zeeman Spacetimes

Zeeman manifolds and their relativistic extensions - the Zeeman spacetimes - are new nonstandard unification models for exploring the quantum physics of point-like and also of extended multiparticle systems. Zeeman manifolds still carry Riemannian metrics on which the unification is realized so that the Hamilton operators, for both type of particle systems, are derived from the very same operator - the Riemannian Laplacian given on Zeeman manifolds. That’s why the latter is called Monistic Hamilton Operator. The relativistic Wave Mechanics is established on Zeeman spacetimes carrying Lorentzian pseudo Riemannian metrics obtained by static resp. accelerating extensions of Zeeman manifolds into the time direction. Their canonical Laplacian is the Monistic Wave Operator from which the wave operators of specific multiparticle systems are derived. Zeeman manifolds and Zeeman spacetimes cover a wide range of examples. The prototypical ones are established on H-type groups and their relativistic extensions, while the most generic ones arise on HyperKähler-Zeeman manifolds and their relativistic extensions. This selfcontained paper explores a unified quantum theory for pointparticle systems to be defined on prototypical Zeeman manifolds and Zeeman spacetimes.