  We revisit the gauge-covariant canonical formalism by separating explicitly
physical and gauge degrees of freedom. We show in particular that the
gauge-invariant linear and angular momentum operators proposed by Chen et al.
can consistently be derived from the standard procedure based on the Noether's
theorem. Finally, we demonstrate that this approach is essentially equivalent
to the gauge-invariant canonical formalism based on the concept of Dirac
variables. Because of many similarities with the background field method, the
formalism developed here should also be relevant to general relativity and any
metric theories.
