Deformations of spacetime and internal symmetries

TL;DR

This paper explores how algebraic deformations of symmetry groups, like quantum groups, can lead to more accurate physical predictions, exemplified by improved baryon mass sum rules matching experimental data.

Contribution

It demonstrates the application of algebraic deformations, specifically quantum groups, to spacetime and internal symmetries, resulting in precise baryon mass predictions.

Findings

Deforming $SU(3)$ to $SU_q(3)$ yields accurate mass sum rules.

Quantum group approach improves agreement with experimental baryon data.

Algebraic deformations generalize symmetry concepts in physics.

Abstract

Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group $SU(3)$ to the quantum group $SU_q(3)\equiv U_q(su(3))$ (a Hopf algebra) and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.