Photon as a Composite Particle in Quantum Electrodynamics

It has been claimed that quantum electrodynamics can be written in a form in which the photon appears as a bound state (of the electron and positron). We examine this notion in the light of recent attempts to describe bound states in field theory by the vanishing of wave-function renormalization constants. Our conclusion is that even if the renormalization constant $Z_3=0\mathrm{}$ to all orders of perturbation theory, the photon cannot be described as a bound state, because other necessary conditions are not satisfied. The argument is given (implicitly) in terms of Green's functions rather than fields.