Photons in media: A second-quantization scheme based on the optical Dirac equation
Phys. Rev. A 114, 042210 – Published 15 October, 2026
DOI: https://doi.org/10.1103/r1vc-w3dl
Abstract
We develop a second-quantization framework for source-free photons based on an optical Dirac-like formulation of Maxwell theory. The analysis applies to the restricted class of spin-degenerate media considered here. The electromagnetic field is recast as a four-component spinorlike wave function containing positive- and negative-frequency branches. The latter, referred to below as the antiphoton branch, is a representation-dependent label and does not describe a new elementary particle or an observable negative-energy photon. Expanding the field in medium-dependent eigenmodes and promoting the mode amplitudes to bosonic operators yields an operator representation analogous to, but physically distinct from, Dirac quantization of electrons. The dielectric tensor produces effective masslike and coupling terms, and the change from the vacuum eigenbasis to the medium eigenbasis can be represented by a boostlike basis transformation; this is not a physical Lorentz boost. Within its stated assumptions, the framework organizes the energy, momentum, angular momentum, helicity, and transverse-spin observables of structured electromagnetic fields in a common representation.
