RECENT MATHEMATICAL DEVELOPMENTS IN THE SKYRME MODEL

In this review we present a pedagogical introduction to recent, more m athematical developments in the Skyrme model. Our aim is to render the se advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects o f the definition of the model. Then we review the instanton method whi ch yields an analytical approximation to the minimum energy configurat ion in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points . We present some explicit results for B = 2. We then describe the wor k done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theo ry. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our o wn work on the semi-classical quantization of nucleon states and low e nergy nucleon-nucleon scattering. (C) 1998 Elsevier Science B.V. All r ights reserved.