Estimate of Quantum corrections to the Mass of the Chiral Soliton in the Nambu–Jona–Lasinio Model

The Bethe–Salpeter equation for pion fluctuations off the chiral soliton in the Nambu– Jona–Lasinio model is constructed. By Goldstone’s theorem this equation has rotational and translational zero modes because the classical soliton is a localized stationary field configuration which violates rotational and translational invariance. Furthermore, the proper normalization of the fluctuating eigen–modes is obtained. Second quantization of the pion fluctuations off the chiral soliton provides an energy functional of the pion fluctuations which formally coincides with that of a harmonic oscillator. The corresponding quantum corrections to the soliton mass together with the semi–classical cranking prescription yield reasonable predictions for the masses of the nucleon and the ∆–resonance when the constituent quark mass is chosen to be about 400MeV. These calculations are, to some extend, hampered by the non–confining character of the Nambu–Jona–Lasinio model. Comments on the 1/NC counting scheme are added. † Supported by a Habilitanden–scholarship of the Deutsche Forschungsgemeinschaft (DFG). 1