Method of statistical operators in the theory of crystals

In [1], a classical statistical theory of a crystal with allowance for the correlations between the motions of its particles was constructed. In the present paper, we consider the quantum case of the statistical thermodynamics of the correlation theory of the crystal state with two-body interaction between particles on the basis of Bogolyubov's method of statistical operators. It is possible to estimate the contribution of the correlation terms and determine the region of applicability of the self-consistent field approximation. The method of statisticaI operators enables one in conjunction with the variational principle to take into account consistently the correction terms to the basic approximation of multiplicity of the binary density matrix.