  We consider a huge quantum system that is subject to the charge
superselection rule, which requires that any pure state must be an eigenstate
of the total charge. We regard some parts of the system as "subsystems," and
the rest as an environment E. We assume that one does not measure anything of
E, i.e., one is only interested in observables of the subsystems. We show that
there exist states with the following properties: (i) Its reduced density
operator is completely equivalent to a vector state of the subsystems for any
gauge-invariant observable of the subsystems. (ii) The vector state is a simple
product of vector states of individual subsystems, each of which is not an
eigenstate of the charge of each subsystem. Furthermore, one can associate to
each subsystem its vector state, which is a pure state, and observables which
are not necessarily gauge invariant in each subsystem. These results justify
taking (a) superpositions of states with different charges, and (b)
non-gauge-invariant operators, such as the order parameter of the breaking of
the gauge symmetry, as observables, for subsystems.
