Spacetime as the Manifold of the Internal Symmetry Orbits in the External Symmetries

摘要

Interactions and particles in the standard model are characterized by theaction of internal and external symmetry groups. The four symmetry regimesinvolved are related to each other in the context of induced grouprepresentations. In addition to Wigner's induced representations of externalPoincar\'e group operations, parametrized by energy-momenta, and the inducedinternal hyperisospin representations, parametrized by the standard model Higgsfield, the external operations, including the Lorentz group, can be consideredto be induced also by representations of the internal hypercharge-isospingroup. In such an interpretation nonlinear spacetime is parametrized by theorbits of the internal action group in the external action group.