The historical development of the Nambu-Jona- Lasinio (NJL) model is briefly reviewed. The SU(2) × SU(2) and U(3) × U(3) local quark NJL models are considered. The mechanisms responsible for spontaneous breaking of chiral symmetry and vector dominance are exhibited. The local NJL model is adequate in describing the mass spectrum and the strong and electroweak decay modes of the four ground-state meson nonets: pseudoscalar, scalar, vector, and axial-vector. The applicability of the model to mesons in a hot dense medium is discussed. It is shown that solving problems related to the description of meson radial excitations and quark confinement requires the nonlocal extension of the NJL model. The primary emphasis of this review is on the methods that are used in various versions of the NJL model. The reader is referred to the cited works for what these models predict in low-energy hadron physics.

PACS: 12.39.−x, 12.40.−y, 25.75.Nq (all) DOI: 10.1070/PU2006v049n06ABEH005905 URL: https://ufn.ru/en/articles/2006/6/a/ 000241498900001 2-s2.0-33750387804 2006PhyU...49..551V Citation: Volkov M K, Radzhabov A E "The Nambu-Jona-Lasinio model and its development" Phys. Usp. 49 551–561 (2006) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI The Nambu – Jona-Lasinio model and its development AU Volkov M K FAU Volkov MK AU Radzhabov A E FAU Radzhabov AE DP 10 Jun, 2006 TA Phys. Usp. VI 49 IP 6 PG 551-561 RX 10.1070/PU2006v049n06ABEH005905 URL https://ufn.ru/en/articles/2006/6/a/ SO Phys. Usp. 2006 Jun 10;49(6):551-561 Оригинал: Волков М К, Раджабов А Е «Модель Намбу-Иона-Лазинио и ее развитие» УФН 176 569–580 (2006); DOI: 10.3367/UFNr.0176.200606a.0569