I was wondering. For fermions someone can find that the Lorentz group is isomorphic to [itex]SU_L(2) \times SU_R(2) [/itex]. However in the Standard Model there is only left-handed neutrinos interacting with the rest of matter. If Lorentz was not partially violated, wouldn't someone expect for the left and right-fermions interacting in the same way? Or am I missing something?