Relativities and Homogeneous Spaces I -- Finite dimensional relativity representations

Abstract

Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and isospin group, on the other side, are discussed under the common concept of "relativity". A relativity is defined by classes $G/H$ of a "little" group in a "general" group of operations.Relativities are representable as linear transformations that are considered for five physically relevant examples.