  A quantum description of the surface waves in an isotropic elastic body
without the use of the semiclassical quantization is proposed. The problem
about the surface waves is formulated in the Lagrangian and Hamiltonian
representations. Within the framework of the generalized Debye model, the
contribution of the surface phonons (rayleighons) to thermodynamic functions is
calculated. It is emphasized that the role of the surface phonons can be
significant and even decisive in low-dimensional systems, granular and porous
media, and that their contribution to the total heat capacity increases with
decreasing temperature.
