Transition from SU (2) L × SU (2) R × U (1) B‐L representation to SU (2) L × U (1) Y by q ‐deformation and the corresponding classical breaking term of chiral U(2)

The minimal Standard Model exhibits a nontrivial chiral U (2) symmetry if the VEV and the hypercharge splitting Δ = ( y   R u ‐ y   R d )/2 of right‐handed leptons (quarks) in a family vanish and Q = T 0 + Y independently in each helicity sector. As a generalization, we start with SU (2) L × SU (2) R × U (1) ( B‐L ) and introduce Δ as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 ⩽ Δ ⩽ 1/2 take the neutral generator of the isospin ½ representation to the singlet representation, i.e. ‘deformes’ the LR representation into the minimal Standard one. The corresponding classical O (3)‐breaking term is a magnetic field perpendicular to the x 3 ‐axis. A simple mapping on the fundamental Drinfeld‐Jimbo q ‐deformed SU (2) representation is given.