  In this study we, remembering the experience with topological Dirac variables
in the non-Abelian Yang-Mills-Higgs (YMH) model with vacuuum BPS monopole
solutions, attempt to construct similar for the Abelian $U(1)$ model. We show
that QED, as one understands it commonly, is only the topologically trivial
sector ($n=0$) of this Abelian $U(1)$ model. For $n\neq 0$ one gets Dirac
monopole modes. In both the cases, $n=0$ and $n\neq 0$, the theory can be
quantized via the Hamiltonian reduction in terms of Dirac variables.
