Semi-relativistic $N$-body quantum mechanics of electrons and photons, with fixed nuclei

Abstract

It is argued that by the end of the 1920s a quantum-mechanical model could have been in place, that not only produces the atomic and molecular energy levels of the many-body Pauli equation with Coulomb interactions and external classical electro- and magneto-static fields without putting these interactions in by hand, but that also accurately describes the interaction of charged particles with electromagnetic radiation, in particular the transitions between atomic or molecular energy levels associated with emission or absorption of radiation. This model suggests a re-interpretation of Maxwell's electromagnetic field equations on spacetime as quantum-mechanical expected values of wave equations on time X configuration space for photons and electrons. The creation / annihilation formalism for photons emerges without invoking second-quantizing the classical Maxwell equations, and without involving the concept of creation / annihilation, thus suggesting an alternative physical interpretation of this formalism. Furthermore, the model suggests that Lorentz covariance of macroscopic physics models emerges through a law of large numbers from a fundamental microscopic model that is not itself Lorentz covariant.