't Hooft's Order-Disorder Parameters and the Dual Potential

preprint1997arXivOpen access

Abstract

It is shown that the operator B(C)=Tr[Pexp⁡ig~∮A~i(x)dxi]B(C) = Tr [P \exp i \tilde{g} \oint \tilde{A}_i(x) dx^i] constructed with the recently derived dual potential A~(x)\tilde{A}(x) and a coupling g~\tilde{g} related to gg by the Dirac quantization condition satisfies the correct commutation relation with the Wilson operator Tr[Pexp⁡ig∮Ai(x)dxi]Tr [P \exp ig \oint A_i(x) dx^i] as required by 't Hooft for his order-disorder parameters.

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