The NJL Model In A Magnetic Background At Finite Temperature

Quantum chromodynamics(QCD)is a theory describing strong interaction among quarks and gluons,it is very successful in high energy region.However,quarks and gluons are confined inside hadrons in the vacuum.QCD cannot be applied perturbatively because the coupling is strong in this energy.It is expected that at sufficiently high temperature and/or density a phase transition will happen---a so called quark-gluon plasma phase in which interacting quarks and gluons form a deconfined gas.Moreover,another important phase transition---chiral phase transition may happen in sufficient temperature and/ or density.Both are very interesting and has been investigating in various models and methods.However,calculations in QCD frame is very difficult.Lattice simulations are based on the first principle therefore their results are taken as standard reference in addition to experiments.But lattice simulations confront considerable difficulty due to so-called sign problems when the chemical potential is large.As in the zero temperature case,effective models are extensively used in the non-zero temperature situation.There are the NJL model which contains quark degrees of freedom only,the linear sigma model and chiral perturbative theory containing purely hadronic degrees of freedom,and the quark-meson model containing both quarks and mesons.They can describe the chiral phase transition but not the deconfinement phase transition,the Polyakov loop is introduced in these models to describe confinement.In this thesis,we will consider the Nambu-Jona Lasinio(NJL)model,which contains only quarks and no gluons so it is not a gauge theory.Interactions in this model are built in order to respect the global symmetries of QCD,the QCD interactions are replaced by effective interactions.The parameters of the NJL model are fixed to reproduce some phenomenological quantity of the QCD vacuum.Therefore,one expects the main characteristics of its phase diagram should represent those of QCD at least qualitatively.NJL model has two shortages,it is not renormalizable and lacks confinement.The Polyakov extended Nambu-Jona Lasinio model(PNJL model)has been introduced to describe confinement and the cut-off from regularization is taken as one of the model parameters.In this thesis we investigate the properties of the NJL model in a magnetic background by using the OPT method and beyond the mean field approximation.We give the chiral condensation and the effective potential at finite temperature and chemical potential with different strength of the magnetic field.The results show that the qualitative properties of thephase diagram are consistent with those of NJL models in the mean field approximation.On the phase boundary two types of phase transitions exist,one is a smooth crossover and the other is a first order phase transition.The magnetic field intensifies the chiral symmetry breaking.With increasing strength of the magnetic field,the critical end point(CEP)shifts to the upper left,that is to say,corresponds to higher critical temperature and lower chemical potential.