Interdimensional effects in systems with quasirelativistic dispersion relations

We examine Green's functions and densities of states for bosons which move in materials with interfaces. Motivated by the interest in materials with quasirelativistic dispersion relations, we demonstrate that modification of Klein-Gordon-type contributions to the Hamiltonian in an interface yields Green's functions and densities of states which exhibit two-dimensional behavior at high energies. Three-dimensional behavior in a low-energy range is recovered if the shift of the mass parameter in the interface is small.