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arXiv · 2510.20049

Photon quantum mechanics with a position observable

Margaret Hawton
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Abstract

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.

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Margaret Hawton. 2025-10-22. Photon quantum mechanics with a position observable. https://arxiv.org/abs/2510.20049

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