An Introduction to Skyrmions as Applied in Nuclear Physics

Abstract

After a very brief discussion of the origins of the Skyrme model for hadronic physics, we treat the form of the effective lagrangian proposed by Skyrme, the nature of the equations of motion derived from it in the hedgehog model, projection techniques for the construction of states referring to nucleons or delta baryons, and the physical properties of these particles as derived from the model. We then explore these same properties with a version of the model that achieves stabilization by omega exchange and extend to other possible terms in the lagrangian. The scene is then prepared for applications of the method to nuclear situations. We begin with a derivation of the nucleon-nucleon potential from the skyrmion model using an extension of the approach of Heitler and London. Unfortunately, this method does not yield the well-known attraction in the central part of the NN potential, and we therefore consider various extensions of the model lagrangian and of the generalized Heitler-London approximation scheme in an attempt to correct this situation. We close with a discussion of the extension of the skyrmion approach to models meant to represent hadronic matter in bulk, including cases pertaining to the special conditions under which a quark-gluon plasma might be formed.

The author’s work in the area of skyrmions has been heavily influenced by his collaboration with R.R. Silbar and G. Kälbermann, who should be seen as partners in the drafting of this series of lectures but share no responsibility for its shortcomings.