Magnetic Monopole in the Loop Representation

TL;DR

This paper quantizes the electromagnetic field with a static magnetic monopole using the loop-representation, revealing surface-dependent wave functionals that vanish under Dirac's quantization condition, simplifying the field's behavior.

Contribution

It introduces a loop-representation approach to magnetic monopoles, showing how surface dependence in wave functionals arises and disappears under Dirac's quantization.

Findings

Wave functional becomes multivalued and surface-dependent in the presence of a monopole.

Surface dependence vanishes when Dirac's quantization condition is satisfied.

Monopole effects on the electromagnetic field are eliminated under quantization condition.

Abstract

We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becomes multivalued, in the sense that it acquires a dependence on the surfaces bounded by the loop. This generalizes what occurs in quantum mechanics in multiply connected spaces. When Dirac's quantization condition holds, this surface-dependence disappears, together with the effect of the monopole on the electromagnetic field.