We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions. The analysis includes the predictions for various hadron properties in vacuum, as well as the study of the features of deconfinement and chiral restoration phase transitions for systems at finite temperature and/or density. We also address other related subjects, such as the study of phase transitions for imaginary chemical potentials, the possible existence of inhomogeneous phase regions, the presence of color superconductivity, the effects produced by strong external magnetic fields, and the application to the description of compact stellar objects.

中文翻译：

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具有非局域可分离相互作用的手性夸克模型在极端条件下的强相互作用物质

我们回顾了具有可分离相互作用的有效非局域 NJL 类手性夸克模型的研究现状，重点关注这种方法在极端条件下强子和夸克物质性质描述中的应用。分析包括对真空中各种强子特性的预测，以及对有限温度和/或密度下系统的解除约束和手性恢复相变特征的研究。我们还讨论了其他相关主题，例如虚化学势的相变研究、不均匀相区的可能存在、彩色超导性的存在、强外部磁场产生的影响，以及在描述紧凑恒星物体。