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A precise formulation of $U(1)$ local gauge invariance in QED is presented,which clearly shows that the gauge coupling associated with the unphysicallongitudinal photon field is non-observable and actually has an arbitraryvalue. We then re-examine the Dirac quantization condition and find that itsderivation involves solely the unphysical longitudinal coupling. Hence aninconsistency inevitably arises in the presence of Dirac monopoles and this canbe considered as a theoretical evidence against their existence. Analternative, independent proof of this conclusion is also presented.Comment: Extended and combined version, refinements added; 20 LaTex pages,  Published in Z. Phys. C65, pp.175-18

Inconsistency of QED in the presence of Dirac monopoles