Restoration of spin and isospin symmetry in the Skyrme model

Abstract

I discuss an approximate application of the collective coordinate quantization method of Christ and Lee to the Skyrme model. The requirement that spin and isospin symmetry be maintained at the collective coordinate level necessitates the introduction of three vibrational degrees of freedom. Qualitatively, the vibrational degrees of freedom enable the magnitude of the pion field to vibrate uniformly between zero and the static classical solution of the Euler-Lagrange equations obtained by Adkins, Nappi and Witten. This effect is characterized by a vibrational frequency that sets the scale of vibrational excitations of the nucleon which are distinct from the spin and isospin excitations of the model. The lowest vibrational excitation of the nucleon is at 616 MeV for the choice of model parameters made by Adkins, Nappi and Witten. This is to be identified with the N ∗ (Roper) resonance. Since this approach requires three vibrational degrees of freedom at a collective level it is not surprising that this estimate for the N ∗ mass is larger than other approaches which introduce just one vibrational degree of freedom. I discuss some qualitative differences and similarities between this approach to the Skyrme model and the non-relativistic quark model and I also discuss some future applications.