The Polyakov, Nambu and Jona-Lasinio model and its applications to describe the sub-nuclear particles

To study the high energy nuclear physics and the associated phenomenon, as the QGP/hadronic matter phase transition, the Nambu and Jona-Lasinio model (NJL) appears as an interesting alternative to the Quantum Chromodynamics, which is not solvable at the considered energies. Indeed, the NJL model allows describing the quarks physics, at finite temperatures and finite densities. Furthermore, in order to try to correct a limitation of the NJL model, i.e. the absence of confinement, it was proposed to couple the quarks/antiquarks to a Polyakov loop: it forms the PNJL model. The objective of this thesis is to see the possibilities offered by the NJL and PNJL models, to describe the relevant sub-nuclear particles (quarks, mesons, diquarks and baryons), to study their interactions, and to proceed to a dynamical study involving these particles.