no the SM is a quantum field theory: particles are excitations of quantum fields, so wave-particle duality is implicit. these fields, at the classical level are function that take a space time coordinate as an argument (space time filling) and typically yields a vector in some vector space (except the higgs field which is a scalar). this vector space in turn is a representation of some symmetry group. the symmetry group of SM is U(1)xSU(2)xSU(3).