The Skyrme model

The so-called skyrmion is a soliton-like classical solution in an effective theory of low-energy mesons (pions, etc.), which is believed to arise from the fundamental interactions at the quark level. Most interestingly, the skyrmion carries a conserved topological charge (to be identified with baryon number) and, in certain cases, needs to be quantized as a fermion (recall that the mesonic fields are all bosonic). This suggests that the lowest energy skyrmion corresponds to the nucleon. Skyrme's remarkable idea then, which dates back to the 1960s, is to view the nucleon as a coherent superposition of mesons. All this, together with some of the necessary background material, is reasonably well explained in the book under review. Hence, it is fair to say that, even though this reviewer has some reservations about part of the presentation, this monograph provides a valuable and informative introduction to a fascinating research topic at the interface of mathematics and elementary particle physics.