Equivalence of Classical Skyrmions and Coherent States of Baryons II. Baryonic Coherent State Construction on Compact Manifolds

Abstract

In connection with the possibility of skyrmion production from small domain disoriented chiral condensates formation from heavy ion collisions, the direct relation of a classical skyrmion to baryon states is examined. It is argued that a skyrmion is a coherent state of baryons. The collective coordinate approach of quantization means that the physical baryon states exist not in flat space but on a compact manifold. This requires the construction of coherent states in such a curve space. Using the techniques associated with the Segal-Bargmann transform also known as the coherent state transform used for example in the study of the classical limit of quantum gravity, such states can be constructed in the context of the Skyrme model. They are made up directly of baryon states on S^3 but with quantum operators on the SO(3) manifold. In terms of wavefunctions, they are a superposition of the analytic baryon wavefunctions of Adkins, Nappi and Witten. The distribution of the baryon states in terms of the relative probabilities of the baryons inside a skyrmion can therefore be determined.