Photons in Media: A Second-Quantization Scheme Based on a Dirac-like Equation

Abstract: Negative-energy states of light are seldom considered in conventional electromagnetic theory. In this work, we introduce a new wave-function representation in helicity space, through which Maxwell's equations are reformulated into a Dirac-like structure. The resulting negative-energy solutions can be interpreted as antiphoton states. Motivated by the Dirac theory of electrons, we further establish a second-quantized framework for photons that is dual to its electronic counterpart. In this framework, the transverse spin of light admits a natural quantum-mechanical interpretation: instead of being described solely as a classical polarization vector, it appears in direct analogy with the intrinsic spin of electrons.