Bridge between hyperbolic and circular symmetry illuminates spacetime spinors
Peter Brands -- Lumina Innovation
In this paper it will be shown that there is a bridge between hyperbolic and circular symmetry, allowing for the derivation of a spacetime spinor. This bridge, based on a hyperbolic rotation with Euclidean angle, reveals a hidden spacetime property - connection between future and past mass-shell - that is obscured when using a hyperbolic angle. The hyperbolic and circular symmetry are connected by a single Euclidean rotation parameter. A full circular rotation in the circular symmetry yields a full rotation in the hyperbolic symmetry, connecting the future and past mass-shell (connecting future and past hyperbola). Thus, the bridge includes passing infinity with a single Euclidean rotation parameter. The spacetime spinor derived from the bridge between hyperbolic and circular symmetry is a solution of the Dirac equation.