Dual Chiral Density Wave In A Magnetic Field

QCD phase diagram gives the properties of strongly interacting substances in equilibrium state.In the temperature-density phase diagram,the longitudinal axis of the phase diagram corresponds to the phase transition at high temperature and low density,i.e.the physical process that can be realized by heavy ion collision.The early evolution of the strongly coupled quark-gluon plasma generated in the ex-periment conforms to the description of relativistic fluids,and many characteristics of the final hadrons are consistent with the prediction of perturbation QCD.The transverse axis of the phase diagram corresponds to the phase transition at low temperature and high density,i.e.the possible physical processes at the core of compact stars.Color superconducting formed by Cooper pairs'condensation is the stable state of quark matter in the region of extremely high density.Whereas in the low temperature and medium density region,we should consider not only the Cooper pair condensation of quarks,but also the chiral conden-sation of quarks on account of the limited chemical potential.And because the strong-coupling constant becomes large in the low temperature and medium density region,the per-QCD is no longer applicable.At the same time,the Lattice QCD is no longer applicable due to the sign problem of fermions,so it is necessary to use various effective models of QCD.At present,there is still no consensus on the ground state of quark matter in medium density region.Depending on the specific physical conditions,different ground states can appear.In addition,considering the relativistic heavy ion collisions and the properties of quark matter in the core of compact stars,one factor that can not be ignored is the existence of strong magnetic fields in both environments,which will have a significant impact on the dynamics of QCD and the properties of quark matter.For example,abnormal transport phenomena in non-centric heavy ion collisions and chiral(inverse)magnetic catalysis effect of QCD,etc.In this thesis,chiral condensation of quark matter is mainly discussed.In the medium density region of the phase diagram,the effective model of QCD and the large N_climit of perturbation QCD predict that the inhomogeneous chiral condensation of quark matter is more stable than the homogeneous chiral condensation.One of the ways to realize inhomogeneous chiral condensation is dual chiral density wave.In this paper,we will mainly discuss the properties of dual chiral density wave in magnetic field and their effects on QCD phase diagrams.NJL model is an effective QCD model commonly used in medium density region.It has the same symmetry group as QCD.At the same time,it also has shortcomings that are a consequence of the use of an effective contact interaction.This interaction is not confining,so it should only be applied to properties for which confinement is not expected to be essential.It also renders the model nonrenormalization,which needs to regulate the theory with regularization schemes.This paper will introduce the characteristics and application of NJL model in detail.In the presence of background magnetic field,the rotational symmetry of space will be destroyed.Fields transformation under vacuum is no longer applicable in the discussion of NJL model.In this paper,we will study the breaking of QCD chiral symmetry by using the Fields transformation which considers the breaking of the rotational symmetry.Its remarkable feature is that the breaking of the rotational symmetry will bring many new condensation channels,one of which is the one related to quark magnetic moment(spin 1).It has been proved in the literature that the spin-1 condensation channel contributes significantly to the color superconductivity of quark matter under very strong magnetic field.In this thesis,we will take into account the spin-1 condensate channel and the dual chiral density wave in the magnetic field,and use the NJL model to obtain the thermodynamic potential of the system under the mean field approximation,so as to obtain the gap equations,and further discuss the phase structure of QCD in the low-temperature and medium-density region.Finally,we calculate the influence of dual chiral density wave of quark matter on photon propagation,and find that there is no shielding effect on the magnetic field,but there is Debye screening on the electric field.The specific form of Debye quality is given in this paper.