A semiclassical representation is introduced to the quantum theory of a strong field, based on a possibility of defining the semiclassical evolution operator in quantum theory, whose effect on the operators of a field and a quantum system transforms them into the solutions of an appropriate semiclassical problem. This representation enables one to go, in a simple way, from a quantum problem to a corresponding semiclassical one, and to use equations of the semiclassical theory as a calculations apparatus in quantum theory and to determine the applicability limits of the semiclassical theory. The possibilities of using the semiclassical representation introduced are illustrated by its use in nonrelativistic quantum electrodynamics.
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