  Methods of large amplitude collective motion in the adiabatic limit are
examined with a special emphasis on conservation laws. We show that the
restriction to point transformations, which is a usual assumption of the
adiabatic time-dependent mean-field theory, needs to be lifted. In order to
facilitate the application of large amplitude collective motion techniques, we
examine the possibility of representing the RPA normal-mode coordinates by
linear combinations of a limited number of one-body operators. We study the
pairing-plus-quadrupole model of Baranger and Kumar as an example, and find
that such representations exist in terms of operators that are state-dependent
in a characteristic manner.
