Localized photon states have non-zero angular momentum that varies with the non-unique choice of a transverse basis and is changed by gauge transformations of the geometric vector potential a. The position operator must depend on the choice of gauge, but a complete gauge transformation of a physically distinct state has no observable effects. The potential a has a Dirac string singularity that is related to an optical vortex of the electric field.

We extend classical Maxwell field theory to a first quantized theory of the photon by deriving a conserved Lorentz four-current whose zero component is a positive definite number density. Fields are real and their positive (negative) frequency parts are interpreted as absorption (emission) of a positive energy photon. With invariant plane wave normalization, the photon position operator is Hermitian with instantaneously localized eigenvectors that transform as Lorentz four-vectors. Reality of the fields and wave function ensure causal propagation and zero net absorption of energy in the absence of charged matter. The photon probability amplitude is the real part of the projection of the photon's state vector onto a basis of position eigenvectors and its square implements the Born rule. Manifest covariance and consistency with quantum field theory is maintained through use of the electromagnetic four-potential and the Lorenz gauge.

We present a new perspective on the link between quantum electrodynamics (QED) and Maxwell’s equations. We demonstrate that the interpretation of the electric displacement vector D = ε 0 E , where E is the electric field vector and ε 0 is the permittivity of the vacuum, as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter runs, as it should.

The properties of the vacuum are described by quantum physics including the response to external fields such as electromagnetic radiation. Of the two parameters that govern the details of the electromagnetic field dynamics in vacuum, one is fixed by the requirement of Lorentz invariance c = 1/ √ ε0µ0. The other one, Z0 = µ0/ε0 = 1/(cε0) and its relation to the quantum vacuum, is discussed in this contribution. Deriving ε0 from the properties of the quantum vacuum implies the derivation of the fine structure constant.