TL;DR
This paper develops a covariant quantum mechanics framework for photons by second quantizing the Fermi Lagrangian, interpreting number density as a probability density, and extending the Hilbert space to include position observables.
Contribution
It introduces a covariant photon quantum mechanics model with a real number density interpreted as a probability density, extending the Hilbert space and Poincare operators.
Findings
Derived a photon continuity equation for creation, propagation, and annihilation.
Established a relationship between this framework and orthodox quantum mechanics.
Proposed a covariant, position-based photon quantum theory.
Abstract
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of fields with norm 1 describing physical photons and the Poincare operators are extended to include position to represent observables. A photon continuity equation is derived that describes creation, propagation and annihilation of photons in an optical circuit. The relationship to orthodox quantum mechanics is discussed.
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