  Four decades ago, Tomonaga proposed the elementary theory of quantum
mechanical collective motion of two-dimensional nuclei of N nucleons. The
theory is based essentially on the neglect of 1/sqrtN against unity. Very
recently we have given exact canonically conjugate momenta to quadrupole-type
collective coordinates under some subsidiary conditions and have derived
nuclear quadrupole-type collective Hamiltonian. Even in the case of simple
two-dimensional nuclei, we have a subsidiary condition to obtain exact
canonical variables. Particularly the structure of the collective subspace
satisfying the subsidiary condition is studied in detail. This subsidiary
condition is important to investigate what is a structure of the collective
subspace.
