  We perform the complete bosonization of 2+1 dimensional QED with one
fermionic flavor in the Hamiltonian formalism. The Fermi operators are
explicitly constructed in terms of the vector potential and the electric field.
We carefully specify the regularization procedure involved in the definition of
these operators, and calculate the fermionic bilinears and the energy -
momentum tensor. The algebra of bilinears exhibits the Schwinger terms which
also appear in perturbation theory. The bosonic Hamiltonian is a local,
polynomial functional of $A_i$ and $E_i$, and we check explicitly the Lorentz
invariance of the resulting bosonic theory. Our construction is conceptually
very similar to Mandelstam's construction in 1+1 dimensions, and is dissimilar
from the recent bosonization attempts in 2+1 dimensions, which hinge crucially
on the presence of a Chern - Simons term.
