Reducible Quantum Electrodynamics. I. The Quantum Dimension of the Electromagnetic Field

In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the Canonical Commutation Relations. The corresponding paradigm is a space-time filled with two-dimensional quantum harmonic oscillators. Mathematically, this is equivalent with two additional dimensions penetrated by the electromagnetic waves.