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Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system. These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics problems, and physicists and chemists studying phenomena related with modern quantum-optical devices.