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

A commentary on single-photon wave function advocated by Bia{\l}ynicki-Birula