Strings and gauge invariance
Kimball A. Milton, Lester L. DeRaad
Source abstract
Within the context of the nonrelativistic theory of dyons, we study a number of interrelated issues concerning the quantum formulation of magnetic charge. We begin by solving the two-body Schrödinger equation for an arbitrarily oriented singularity line (string) in terms of the known solutions with the string on the z axis. Charge quantization conditions emerge by requiring that the wavefunctions be single valued. The general solutions express the necessary gauge covariance of the wavefunctions. These results provide a basis for the reconsideration of the phase factor in the dyon–dyon scattering amplitude. Finally, the connection between the formulations in terms of vector potentials and in terms of intrinsic spin is investigated. This approach leads to a rederivation of the gauge transformation properties of the theory.
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