Abstract Without use of pathintegral formalism a composite particle effective dynamics is developed for spinor quantum electrodynamics. By algebraic evaluation of spinor quantum electrodynamics in Coulomb gauge a corresponding functional equation is derived. The commutation rules for the transversal electromagnetic field can be deduced as a consequence of this formalism. By application of weak mapping theorems the QED functional equation can be mapped onto a functional equation for composite particles with mutual interaction and interaction with the electromagnetic field. The formalism is demonstrated for positronium states. The incorporation of renormalization into this scheme is verified.