A first quantized theory of the photon is developed that incorporates all of the usual rules of quantum mechanics. The state vector is argued to be proportional to the four-vector potential. Scalar products and the probability amplitude are invariant under gauge transformations that satisfy the Lorentz gauge condition. The eigenvectors of a recently constructed Hermitian position operator with commuting components provide a basis for the position representation.
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Margaret Hawton (1999) studied this question.
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