defines the unbroken part of the gauge group, where Q is the electric charge, T 3 is the generator of rotations around the 3-axis in the SU (2) and Y W is the weak hypercharge generator of the U (1). This combination of generators (a 3 rotation in the SU (2) and a simultaneous U (1) rotation by half the angle) preserves the vacuum, and defines the unbroken gauge group in the standard model, namely the electric charge group. The part of the gauge field in this direction stays massless, and amounts to the physical photon. By contrast, the broken trace-orthogonal charge T 3 − − 1 2 Y W = 2 T 3 − − Q couples to the massive Z boson.