  We present in this paper how the single-photon wave function for transversal
photons (with the direct sum of ordinary unitary representations of helicity 1
and -1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the
quantized free electromagnetic field. Rigorous Gupta-Bleuler quantization of
the free electromagnetic field is based on our generalization (published
formerly) of the Mackey theory of induced representations which includes
representations preserving the indefinite Krein inner-product given by the
Gupta-Bleuler operator. In particular it follows that the results of
Bia{\l}ynicki-Birula on the single-photon wave function may be reconciled with
the causal perturbative approach to QED.
