Interaction of conduction electrons with an esternal electromagnetic in the gage-invariant theory of combined resonance

A study is made of the structure of the Hamittonian for the interaction of conduction electrons with an electromagnetic field for semicondueting crystals whose Hamiltonian contains terms that depend on both the spin and the kinetic degrees of freedom of the electrons. It is shown that the previously constructed [1] interaction Hamiltonians for such systems break the gage invariance of the equations of motion of the physical quantities. By means of a time-dependent canonical transformation of the system's Hamiltonian, a new expression is found for the operator of the interaction with the field, and this preserves the gage invarianee of the equations of motion. Canonical ransformations of the basis operators in the nonequilibrium statistical operator method are considered. Expressions that are exact with respect to the internal interactions of the subsystems are constructed for the power absorbed by the electrons in the second order in the strengths of the electric and the magnetic field.