Hi, 1: I just want to ask that what does SU(3) x SU(2) x U(1) means? and when a lagrangian is invariant under SU(3) x SU(2) x U(1) what does that mean? Does it mean that lagrangian L is invariant under SU(3) and then SU(2) and then U(1)? so if one wants to check SU(3) invariance of L then one operates with an element of SU(3) and leave the rest? doesent it operate on electro-weak part of L? 2: Suppose that I have total standard-model Lagrangian for fermions as: L(sm) = L(qcd) + L(Electro-weak)............(left handed) where fermions in L(qcd) are triplets and fermions in L(electro weak) are doublets SEPARATELY which means that the generator of SU(3) = 3x3 matrices and generators of SU(2) = 2x2 matrices SEPARATELY. How can I arrange these different dimension matrices in the above lagrangian? which would be valid for leptons as well as quarks? Actually my main confusion is that how can the same lagrangian be valid for leptopns in doublets, quakrs in triplets and generators in 3x3 and 2x2 matrices. But what about the U(1) matrix? If I take only QCD SU(3) lagrangian and write it next to Electro-weak SU(2) x U(1) lagrangian, is this OK for SU(3) x SU(2) x U(1) complete lagrangian? there will be a mismatch in dimension of matrices though or not? At least, I need the dimensions of different terms in a simple QCD -Elec-Weak lagrangian (as above) for left handed leptons and then left handed quarks to remove my confusions. many thanks.