Equivalence of Classical Skyrmions and Coherent States of Baryons I. Constrained Quantization on the SU(2) and SO(3) manifolds

In the Skyrme model, the Lagrangian can be quantized in several ways using the collective coordinate approach. Not all of which produce quantum states that can be interpreted as physical particles. For example the SU(2) collective coordinate approach produces both integral and half-integral spin and isospin states. Only half of these are the physical baryons. Less well known is the fact that it is equally possible to quantize the system using the SO(3) collective coordinates. This produces only unphysical integral spin and isospin states. To fulfill the goal of being able to express a classical skyrmion as a coherent state of baryons directly in terms of the baryon states, surprisingly a combination of both collective coordinate approaches is required. To prepare for the subsequent application to skyrmion formation through disoriented chiral condensates in heavy ion collisions, the Skyrme model is rigorously quantized using the Dirac prescription for constrained systems. This is shown for both the SU(2) as well as the SO(3) collective coordinate approach.