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Reduction formulas for coherent states.

The Lehmann-Symanzik-Zimmermann reduction formulas consistent with the use of asymptotic coherent states to model external fields are developed for the case that the in-state external field differs from the out-state external field. It is shown for the specific choice of coherent state considered that the reduction formulas deviate from the standard forms presented in textbooks. The coherent states are not reduced directly but instead are incorporated into the perturbative representation of the time-ordered product. An effective potential created by the coherent state is found which self-consistently determines the form of the asymptotic field. An application is made to the case of nonrelativistic quantum electrodynamics in a laser pulse.