The principal frame of the formalism is based on an algebraic construction
introduced first by Gelfand, Neimark and Segal. Several publications
strongly encourage a further extension of the formalism aiming at a uniform
and elegant description of the nuclear collective motion together with the
possible underlying symmetries.
We would like now to apply the formalism to a systematic analysis
of the rotational spectra and couplings of the rotational motion to other,
first of all quadrupole and octupole vibrations. By analyzing various possible
model-symmetries introduced to the formalism we hope to learn about the
isospectral bands.
We would like to examine in detail the problem of the existence
of all quantum numbers that may characterize collective modes; we would like
to study this problem of symmetry by re-examining some of the most successful
nuclear models (generalized Bohr model, algebraic model of Rowe and Rosentsteel,
and the Interacting Boson Approximation).