  I discuss the momentum and angular momentum decomposition problem in the
Abelian Higgs model. The usual gauge-invariant extension (GIE) construction is
incorporated naturally into the framework of quantum gauge transformation
$\grave{a}$ ${\it la}$ Strocchi and Wightman and with this I investigate the
momentum and angular momentum separation in a class of GIE conditions which
correspond to the so-called "static gauges". Using this language I find that
the so-called "generator criterion" does not generally hold even for the
dressed physical field. In the case of $U(1)$ symmetry breaking, I generalize
the standard GIE construction to include the matter field degrees of freedom so
that the usual separation pattern of momentum and angular momentum in the
unitarity gauge can be incorporated into the same universal framework. When the
static gauge condition could not uniquely fix the gauge, I show that this GIE
construction should be expanded to take into account the residual gauge
symmetry. In some cases I reveal that the usual momentum or angular momentum
separation pattern in terms of the physical dressed field variables needs some
type of modification due to the nontrivial commutator structure of the
underlying quantum gauge choice. Finally, I give some remarks on the general
GIE constructions in connection with the possible commutator issues and
modification of momentum and angular momentum separation patterns.
