kqrepresentation in lattice dynamics

The $\mathrm{kq}$ representation is introduced into lattice dynamics. As in electron dynamics it turns out to be useful both conceptually and for calculational purposes. An integral effective-mass-like equation is derived. It is shown to reproduce the well-known results for localized impurities in lattice dynamics. Similarly the $\mathrm{kq}$ representation can be introduced into the description of magnons.