# [Recommendation] QCD and the Skyrme model

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The Skyrme model is an interesting approximation to QCD in which fermions appear as solitons in a purely bosonic quantum field theory. As such it features various topological issues in QFT. I just came across the following book on the topic:

V.G. Kakhankov, Y.P. Rybakov and V.I. Sanyuk, The Skyrme model: Fundamentals Methods Applications, Springer, Berlin 1993.

It discusses  in a very thorough manner the Skyrme model, its properties, its quantization, its relations to QCD, and applications to meson and baryon modeling.

Part III on hadron physics applications starts off with an introduction from which the following is taken [pp.130-131,137]:

The mathematical difficulties grow exponentially when one approaches the most interesting for practical purposes the low energy region of QCD. This region, which in principle contains all Nuclear Physics phenomena, in particular should provide us with the information on the masses, lifetimes, magnetic moments, sizes, scattering rates, and other properties of strongly interacting particles. At present this is not the case, as there is no a systematic method for treating the low energy QeD and for extracting the necessary information [...] The connection between the asymptotic freedom domain and the phase of confinement presents an almost insurmountable problem, despite of some progress of lattice calculations, and there seems to be not much hope in the nearest future. These attempts to get the whole picture of strong interactions in terms of quarks and gluons overshadowed for more than decade the visible achievements of the phenomenological (or effective) Lagrangian approach. The latter approach, developed on the basis of current algebra in 1960's, in spite of its relative simplicity enabled one to obtain some reasonable answers for hadron observables. [...] The derivation of effective actions (e.g. generalized Skyrme models) from the QED fundamental Lagrangian (9.4) is a problem of much conceptual and practical relevance.

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