## Photonic Equations of Motion

Description:
Although the concept of the photon as a quantum particle is sharpened by the quantization of the energy of the classical radiation field in a cavity, the photon's spin has remained a classical degree of freedom. The photon is considered a spin-1 particle, although only two classical polarization states transverse to its direction of propagation are allowed. Effectively therefore the photon is a spin-1/2 particle, although it still obeys Bose-Einstein statistics because the photon-photon interaction is zero. Here they show that the two polarization states of the photon can be quantized using Pauli's spin vector, such that a suitable equation of motion for the photon is Dirac's relativistic wave equation for zero mass and zero charge. Maxwell's equations for a free photon are inferred from the Dirac-field formalism and thus provide proof of this claim. For photons in the presence of electronic sources for electromagnetic fields we posit Lorentz-invariant inhomogeneous photonic equations of motion. Electro-dynamic operator equations are inferred from this modified Dirac-field formalism which reduce to Maxwell's equations if spin-dependent terms in the radiation-matter interaction are dropped.

Date:
September 17, 2004

Creator:
Ritchie, A B & Crenshaw, M E

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