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

TL;DR

This paper explores a novel interpretation of spacetime as the manifold of internal symmetry orbits, linking internal and external symmetries in the standard model through induced group representations.

Contribution

It introduces a new perspective where nonlinear spacetime is parametrized by internal symmetry group orbits within external symmetry groups.

Findings

Spacetime can be viewed as the manifold of internal symmetry orbits.

External symmetries are induced by internal hypercharge-isospin group representations.

Provides a unified framework connecting internal and external symmetries in particle physics.

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 Poincar\'e 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 be considered to be induced also by representations of the internal hypercharge-isospin group. In such an interpretation nonlinear spacetime is parametrized by the orbits of the internal action group in the external action group.