Inconsistency of QED in the Presence of Dirac Monopoles II

Abstract

We enlarge the local gauge invariance of QED from $~U(1)_A~$ to $~U(1)_A \times U(1)_Θ~$ by introducing another unphysical pure gauge field $~Θ~$ 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 $~U(1)_Θ~$ group. The unique physically consistent solution of these two DQCs is a vanishing magnetic charge, which implies that no Dirac monopole exists in nature.