A Topologically Stable Solution in Quantum Electrodynamics

TL;DR

This paper presents a novel exact classical solution in quantum electrodynamics formulated in higher-dimensional space, featuring a topologically stable, localized electromagnetic field resembling a point charge with quantized charge.

Contribution

It introduces a new topologically stable classical solution in QED in 4+2 dimensions, expanding the understanding of possible field configurations and their quantization.

Findings

Solution is stationary and localized around a topological singularity.

Electromagnetic field corresponds to a point electric charge.

Charge is quantized and determined by the coupling constant.

Abstract

This paper constructs exact classical solutions of the equations of QED. These are constructed in 4+2 dimensional space, which fibers over the usual 3+1 dimensional space-time. The solution is stationary and localised about a topological singularity in space time. The electromagnetic field is that of a point electric charge, positioned at the singularity. Away from the singularity, all the conserved currents vanish. The solution comes in 8 varieties, corresponding to any choice of positive or negative charge, spin or mass (though it is presumed that the negative mass solutions are not physical). The charge is quantised, and determined up to sign by the coupling constant in the theory. The main element in the construction is simply the requirement that the solution be rotationally symmetric.