Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model

The description of baryons as chiral solitons of the Nambu--Jona--Lasinio (NJL) model is reviewed. A motivation for the soliton description of baryons is provided from large $N_C$ QCD. Rigorous results on the spontaneous breaking of chiral symmetry in QCD are discussed. It is then argued that the NJL model provides a fair description of low--energy hadron physics. The NJL model is therefore employed to mimic the low--energy chiral flavor dynamics of QCD. The model is bosonized by functional integral techniques and the physical content of the emerging effective meson theory is discussed. In particular, its relation to the Skyrme model is established. The static soliton solutions of the bosonized NJL model are found, their properties discussed, and the influence of various meson fields studied. These considerations provide strong support of Witten's conjecture that baryons can be understood as soliton solutions of effective meson theories. The chiral soliton of the NJL model is then quantized in a semiclassical fashion and various static properties of the nucleon are studied. The dominating $1/N_C$ corrections to the semiclassically quantized soliton are investigated. Time--dependent meson fluctuations off the chiral soliton are explored and employed to estimate the quantum corrections to the soliton mass. Finally, hyperons are described as chiral solitons of the NJL model. This is done in both, the collective rotational approach of Yabu and Ando as well as in the bound state approach of Callan and Klebanov.