It has been shown that it is possible to establish relations between some properties of quarks and leptons (including sterile neutrinos) and spin representation of multidimensional linear canonical transformations. In this approach, the electric charge, weak hypercharge and weak isospin of the particles are expressed as linear combinations of some operators defined from the generators of the Clifford algebra associated with the spin representation of linear canonical transformations. The existence of Color charge is also explained in this framework.