  We reexamine a unitary-transformation method of extracting a physical
Hamiltonian from a gauge field theory after quantizing all degrees of freedom
including redundant variables. We show that this {\it quantum Hamiltonian
reduction} method suffers from crucial modifications arising from
regularization of composite operators. We assess the effects of regularization
in the simplest gauge field theory, the Schwinger model. Without
regularization, the quantum reduction yields the identical Hamiltonian with the
classically reduced one. On the other hand, with regularization incorporated,
the resulting Hamiltonian of the quantum reduction disagrees with that of the
classical reduction. However, we find that the discrepancy is resolved by
redefinitions of fermion currents and that the results are again consistent
with those of the classical reduction.
