1) Which U(1), SU(2) and SU(3) gauge invariances are implemented in nature according to the Standard Model? What are the related quantum numbers?
2) The SU(2) symmetry is referred to as a non-abelian symmetry. What does this imply for the interactions between the force carriers?
3) Give the expression for a SU(3) local gauge transformation acting on a quark spinor triplet.
2. The attempt at a solution
1) Gauge symmetries in the SM, used describe three of the fundamental interactions, are based of the SU(3)xSU(2)xU(1) group. Roughly speaking the symmetries of the SU(3) group describe the stronge force, the SU(2) group the weak interaction and U(1) the electromagnetic force.
2) The electroweak model breaks parity maximally. All its fermions are chiral Weyl fermions, which means that the charged weak gauge bosons only couple to left-handed quarks and leptons (making this a non-abelian symmetry).