According to a post on a mailing list here: https://groups.google.com/d/msg/sci.physics.research/n7Ao7N9aeq0/wqgj20-jBQAJ
In general, quatum states |Psi> of the electromagnetic field, no matter if free radiation field or interacting field, can be represented as wave functionals
Psi[A^mu(x),t]
on the space of classical field configurations A^mu(x).
What does a one-photon state look like when expressed as such a wave functional? I have tried to develop the theory myself by canonically quantizing the field, but I'm stuck because I can't figure out how to mathematically work with such wave functionals---they belong to some confusing uncountably-dimensional vector space.
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