Quantum statistical theory of interaction of an electromagnetic field with a many-level system. I

The interaction of an electromagnetic field with a many-level system is considered by the method of density matrix expansion with respect to an orthonormalized system of operators formed by irreducible unitary representations of Lie groups, the algebra of which is used for the construction of the total Hamiltonian of the system. The explicit form of the density matrix (without taking account of dissipation), response function and the average values of the dynamic operator are obtained without the use of approximations associated with the intensity of external fields.