International Journal of Theoretical Plo'sics. l'oL 23. No. & 1084 Geometric Quantization in Many-Body Physics George Rosensteel Department of Pto'sics attd Quantum TheotT Group. Tulane Unit,ersi(l'. New Orleans. Louisiana 70118 Received October 1. 1083 The Bohr-Mottelson model of nuclear rotations and vibrations is a cornerstone of nuclear structure physics (Bohr et al., 1976). The model regards the nucleus as a liquid drop deformed into an ellipsoid which rotates and incompressibly vibrates, thereby giving rise to rotational bands and strong electric quadrupole transitions. By experiment, one can de- termine the shape from the intrinsic quadrupole moments and measure the nuclear moment of inertia from the energy levels. The success of this model stems not only from its generally favorable agreement with experiment, but also from the transparent geometrical view it provides of the nucleus. Nevertheless, the Bohr-Mottelson model has inherent limitations. In order to explain detailed nuclear properties it is obvious that we need to incorporate noncollective features of the nucleus, e.g., shell structure, into our model. But, how can we relate the liquid drop picture to the microscopic view of the nucleus as an interacting system of neutrons and protons? At the 1970 Solvay Conference, Professor Wigner emphasized the importance of answering this question for nuclear structure physics (Wigner, 1970). We need to be able to pose and solve nuclear structure problems with as much precision and detail as is necessary, but not at the expense of obscuring the fundamental geometrical properties of the nucleus. The resolution of this dilemma involves ideas from geometric quantiza- tion and dynamical groups which have parallels with the relativistic free particle. As we shall see, the absence of a theory of interacting relativistic particles does not allow us to pursue the correspondence to its ultimate conclusion. However, we will succeed in embedding the liquid drop model into the existing theory of interacting nonrelativistic neutrons and protons, thereby resolving the Solvay question. 777 (X)20-7748/84/(]80(1-0777503.50/0 ' 1984 Plenum Publishing Corporation