Algebraic Resonance Perturbation Theory in Problems of Nonlinear and Quantum Optics

The algebraic resonance perturbation theory (ARPT) is formulated, general expressions of the theory are written down, by means of which effective Hamiltonians are concisely derived, interference interactions are described, and kinetic equations are obtained for various cases of interaction between electromagnetic radiation and quantum systems. The natural integration of the method of stochastic differential equations into ARPT and the physical justification of the principles for the selection of ARPT terms are indicated in the case of approximating the environment of an open system by delta-correlated noise. The inevitability of the emergence of interference interactions is emphasized due to the formulated ARPT requirements regarding the selection of only slowly time-varying terms in the Dirac picture into the effective Hamiltonian.