Inconsistency of QED in the Presence of Dirac Monopoles II

Abstract

We enlarge the local gauge invariance of QED from $U(1{)}_A$ to $U(1{)}_A\times U(1{)}_{\Theta }$ by introducing another unphysical pure gauge field $\Theta$ with an independent, unphysical gauge coupling $\tilde{e}$. This pure gauge field can be gauge-transformed away and the resulting theory is {\it identical to} standard QED. We then re-examine the Dirac quantization condition (DQC) for point monopoles and find that two essentially different DQCs can be derived. One DQC involves a gauge coupling $e$ in the $U(1{)}_A$ group and the other only the unphysical gauge coupling $\tilde{e}$ in the $U(1{)}_{\Theta }$ group. The unique physically consistent solution of these two DQCs is a vanishing magnetic charge, which implies that no Dirac monopole exists in nature.

Comments: Pages: 8; Report#: VPI-IHEP-93-13