Canonical quantization of the Skyrme model

The canonical quantization of the Skyrme model is presented. Due to the complexities of the original set-up, first postulated by Rajeev, a new set of fields is found which satisfy a Lie algebra and for this reason, simplifies the study of the system. Using the new fields, the properties of the states under rotations are examined. As a result we re-derive the quantization of the coefficient of the Wess-Zumino action as an a priori consistency condition. We also find under what circumstances states with non-vanishing winding number behave like fermions.     

Recent mathematical developments in the Skyrme model

In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration 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 work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. 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 own work on the semi-classical quantization of nucleon states and low energy nucleon–nucleon scattering.     

Multisolitons in a two-dimensional Skyrme model

The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and derive an expression for the interaction potential of two solitons which only involves the solitons' asymptotic fields. If the solitons have topological degree 1 or 2 there are simple formulae for their interaction potentials which we use to prove the existence of solitons of higher degree. We explicitly compute the fields and energy distributions for solitons of degrees between one and six and discuss their geometrical shapes and binding energies.     

Meson exchange currents in the Skyrme soliton model

The isovector meson exchange currents are investigated on the basis of the product ansatz in the Skyrme model. It is shown that the standard one-pion-exchange currents are correctly reproduced as a limiting approximation to more general expressions derived here. We discuss interesting consequences of the spatially extended structure of the nucleon, which is naturally incorporated in the present treatment. It is also pointed out that there exists a simple analytical relation between the isoscalar exchange current of the Skyrme model and the standard ρπγ exchange current.     

Bound-state approach to strangeness in the Skyrme model

We show that baryons carrying heavy flavors, such as strangeness and charm, can be described by bound states of the corresponding heavy mesons in the background field of the basic SU(2) skyrmion. This method is quantitatively successful to O(N_c⁰), in the sense of the large-N_c expansion, but at O(1/N_c) it experiences problems associated with our lack of knowledge of higher-derivative terms in the Skyrme action. We derive a model-independent mass relation for strange baryons which is in excellent agreement with experiment.     

Photoproduction of baryon resonances in the Skyrme model

We compare the photoproduction helicity amplitudes calculated from the Skyrme model with experimental curves for L_π ⩽ 3 up to k_γ ⩽ 1.25 GeV. In most cases the model gives a good account of structure, size and phases of the measured data.     

Static properties of nucleons in the Skyrme model

We compute static properties of baryons in an SU(2) × SU(2) chiral theory (the Skyrme model) whose solitons can be interpreted as the baryons of QCD. Our results are generally within about 30% of experimental values. We also derive some relations that hold generally in soliton models of baryons, and therefore, serve as tests of the $\text{1}\text{N}$ expansion.