Three approaches to nuclear and hadronic collective motion are reviewed, compared and contrasted: the standard symmetry approach as typified by the Interacting Boson Model, the kinematic symmetry group approach of Gell-Mann and Tomonaga, and the recent direct construction

Three approaches to nuclear and hadronic collective motion are reviewed, compared and contrasted: the standard symmetry approach as typified by the Interacting Boson Model, the kinematic symmetry group approach of Gell-Mann and Tomonaga, and the recent direct construction by Buck. (Invited paper presented at the Symposium on Group Theory and Its Applications in Physics, Cocoyoc, Morelos, Mexico, January 10-12, 1982.) * Work supported in part by the Department of Energy under contract DE-AC03-76SF00515 and by the National Science Foundation. t Permanent address: Duke University, Durham, N.C. 27706.