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In this review article, we give overview on the extended chiral quark models.In particular, how these models are extended to include the higher-orderinteractions, quantized fields, logarithmic potential and the effect of thesemodifications on hadron properties at hot and dense mediums. In addition, howwe deal with non-normalization of the Nambu-Jona-Lasinio (NJL) model by usingmid-point technique. Therefore, the extended quark models give satisfiedresults in comparison with lattice QCD at finite temperature and baryonicchemical potential. The extra effort is needed to deal with chiral quark modelsin the presence of external magnetic field at finite temperature and density.

Extended Chiral Quark Models in the Framework of Quantum Chromodynamic: Theory and their Applications in Hot and Dense Mediums