  New phenomenological approach for the description of elementary collective
excitations is proposed. The crystal is considered to be an anisotropic
space-time vacuum with a prescribed metric tensor in which the information on
electromagnetic crystalline fields is included. The quasiparticles in this
space are supposed to be described by the equations structurally similar to the
relativistic wave equations for particles in empty space. The generalized
Klein-Gordon-Fock equation and the generalized Dirac equation in external
electromagnetic field are considered. The applicability of the proposed
approach to the case of conduction electron in a crystal is discussed.
