Geometrical interpretation of isospin subalgebras in SU(3)

Abstract

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are [Formula: see text], [Formula: see text] and [Formula: see text] isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.