Deformations of spacetime and internal symmetries

Niels G Gresnigt,Adam B Gillard,L Bravina,Y Foka,S Kabana

doi:10.1051/epjconf/201716407009

Niels G Gresnigt, Adam B Gillard + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/201716407009

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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.

Highlights

In this short article we discuss some of the applications of algebraic deformations to spacetime and internal symmetries
The combined Poincaré-Heisenberg Lie algebra structure that underlies the standard model (SM) may be deformed to a semi-simple algebra through the introduction of two additional fundamental length scales, at which point there no longer exist any non-trivial deformation within the category of Lie algebras and so no further fundamental scales can be introduced
As a specific example of the application of q-deformations to internal symmetries, we consider a recent result by one of the authors that shows that replacing the flavor symmetry group S U(3) by its quantum group counterpart S Uq(3) and accounting the for mass splittings within baryon isospin multiplets leads to octet and decuplet baryon mass formulas of exceptional accuracy

Summary

Introduction

In this short article we discuss some of the applications of algebraic deformations to spacetime and internal symmetries. As a specific example of the application of q-deformations to internal symmetries, we consider a recent result by one of the authors that shows that replacing the flavor symmetry group S U(3) by its quantum group counterpart S Uq(3) and accounting the for mass splittings within baryon isospin multiplets leads to octet and decuplet baryon mass formulas of exceptional accuracy. We consider this as strong evidence for the conjecture that quantum groups play an important role in high energy physics

Lie-type deformations and the importance of stability

Lie-type deformations of spacetime symmetries

Singleton physics

Findings

Conclusion