On the gauge groups of particle physics and their quantum deformations

Abstract:
All the forces of Nature are actually understood as mediated by an exchange of gauge fields of the symmetry group SU(3) ÄSU(2) ÄU(1). Such a gauge principle then describes the very important field called "particle (or high energy) physics" and its famous "Standard Model" relating strong, electromagnetic and weak (or strong and electroweak) interactions. Knowing that the quantum deformations of such unitary local symmetry groups as well as their irreducible representations have been studied in a relatively recent past, we propose to visit a corresponding "q-Standard Model". Such a step is seen as a first part of our general programme and will be useful in a second one coming back on öld current algebras and associated sum rules" based on chiral symmetry groups such as SU(2) ÄSU(2) and SU(3) ÄSU(3). Here we plan to introduce the main useful ingredients for these purposes but by taking the qu-ified version of SU(2) as the typical example.