Spacetime as Manifold of Internal Symmetry Orbits in External Symmetries

Abstract

Interactions and particles in the standard model are characterized by the action of internal and external symmetry groups. The four symmetry regimes involved are related to each other in the context of induced group representations. In addition to Wigner's induced representations of external Poincare group operations, parametrized by energy-momenta, and the induced internal hyperisospin representations, parametrized by the standard model Higgs field, the external operations, including the Lorentz group, can also be considered to be induced by the internal operations of the hypercharge–isospin group. In such an interpretation nonlinear spacetime is parametrized by the orbits of the internal action group in the external action group.