A new formalism is developed for the description of the electromagnetic field interaction with a crystal. The main characteristics of the proposed approach are the energy and momentum density of the field. The reaction of the environment to an external perturbation is considered as a local change in the geometry, which consists in the rotation of an orthogonal basis built on the induction vectors and the field momentum. In this case, the geometric characteristics are determined by the structural parameters of the medium. Fundamental equations in the local basis are obtained. As shown, the separation of waves by polarization, when considering problems of X-ray wave scattering on a crystal, is not quite correct even in the case of an ideal crystal. General equations are obtained that allows one to calculate the momentum and energy of a field when it interacts with a crystal.