A gauge theory was developed which described, within the continuum approximation, the behavior of dislocations, disclinations, and elastic fields in crystals with multi-atomic lattices. The use of the SO(3N)T(3N) group, where N was the number of atoms in the unit cell of the crystal and  was the semi-direct group product operation, as a gauge group was supported. The formulae for the elastic fields of dislocations and disclinations, that corresponded to both acoustic and optical phonon modes, were obtained in terms of the Green’s function of the basic equations of elasticity theory for a multi-atomic crystal. The Lagrangian for the interaction of defects with elastic fields was constructed, and the basic theoretical equations were derived.

A.I.Moussienko, V.A.Koptsik: Kristallografiya, 1996, 41[4], 586-90 (Crystallography Reports, 1996, 41[4], 550-4)