2025/10/22 by Margaret Hawton, Hawton, Margaret
#quant-ph
paper · pdf · doi:10.48550/arxiv.2510.20049
We second quantize an explicitly Lorentz invariant lagrangian density and derive a theory of photon quantum mechanics. The one photon Hilbert space is the vector space of normalizable positive frequency four-potentials. Observables are described by the Poincare operators augmented with a photon position operator. It is found that the probability amplitude to observe a photon in a bounded region of space, defined as the projection of the four-potential onto the basis of position eigenvectors, equals the inverse Fourier transform of the probability amplitude for a plane wave. A continuity equation that describes photon propagation in free space and an optical circuit is derived.