Institute of Physics, University of Liege,

Liege, BELGIUM

E-mail: Jules.Beckers@ulg.ac.be

**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.