THE EXTRA GAUGE SYMMETRY OF STRING DEFORMATIONS IN ELECTROMAGNETISM WITH CHARGES AND DIRAC MONOPOLES

Abstract

We point out that electromagnetism with Dirac magnetic monopoles harbors an extra local gauge invariance called monopole gauge invariance. The gauge transformations act on a gauge field of monopoles [Formula: see text] and are independent of the ordinary electromagnetic gauge invariance. The extra invariance expresses the physical irrelevance of the shape of the Dirac strings attached to the monopoles. The independent nature of the new gauge symmetry is illustrated by comparison with two other systems, superfluids and solids, which are not gauge-invariant from the outset but which nevertheless possess a precise analog of the monopole gauge invariance in their vortex and defect structure, respectively. The extra monopole gauge invariance is shown to be responsible for the Dirac charge quantization condition 2eg/ħc=integer, which can now be proved for any fixed particle orbits, i.e. without invoking fluctuating orbits which would correspond to the standard derivation using Schrödinger wave functions. The only place where quantum physics enters in our theory is by admitting the action to jump by 2πħ×integer without physical consequences when moving the string at fixed particle orbits.