Study Of Finite Temperature And Finite Density QCD By Dyson-Schwinger Equation And A Model Study Of Quark Star

Quantum Chromo dynamics(QCD)is the theory of strong interactions and has abundant fascinating dynamical properties.Because of its remarkable nonperturba-tive characters in the low energy regions such as colorconfinement,dynamical chiral symmetry breaking(DCSB),non-trival vacuum structures,nonperturbative approach-es are needed in the study of QCD.The strong interaction processes almost take place at finite temperature and density and the study of the interactions,phase structure and phase transitions of hadronic matter at finite temperature and density can provide more clues to and tests of high energy physics experiments and astronomical observations.The study of properties of strong interacting matter at finite temperature and density is the focus of both theoretical and experimental high energy physics.In quantum field theory(QFT),the n-point Schwinger functions,particularly two-point functions,play a key role in describing the properties and dynamical behaviors of the system.In this thesis some relations between the n-point Schwinger functions and hadronic quantities based on QCD are found.We have discussed the vacuum susceptibility,the quark number susceptibility and the equation of state(EOS)of QCD.Dyson-Schwinger equations(DSE),a nonperturbative Poincare invariant contin-uum approach to solve QCD,provide a systemic framework of dealing with not only nonperturbative phenomena such as color confinement and DCSB but also hadronic structures.The study of properties of hadronic matter at finite temperature and densi-ty is a common concern of theoretical physics,high energy physics,astrophysics and cosmology.In the framework of rainbow approximation of the Dyson-Schwinger ap-proach,we develop an effective method for calculating the dressed quark propagator at small chemical potential ? and give the relations between the dressed quark propagator at ??0 and the one at ?=0.We also prove that this conclusion is valid at finite temperature T and obtain the relations between the quark propagator at ??0,T?0 and the propagator at ?=0,T?0.In this thesis,working in the framework of Dyson-Schwinger equations and em-ploying a range of znsatze for the full fermion-photon vertex of a range of QED3,we study the interplay between explicit and dynamical chiral symmetry breaking in QED3.In the case of nonzero fermions mass,it is found that,besides the ordinary solution,the fermions gap equation has another solution which has not been reported in the pre-vious work of QED3.In the low energy region,one observes that these two solutions are apparently different,but in the high energy region they coincide with each other.In addition,it is found that this solution exists only when the mass is small than a critical value.The critical mass decreases apparently with the rise of the number of fermion flavors and vanishes at a critical values NC,which corresponds to thye critical number of fermion flavors of QED3 in the chiral limit.It is an interesting phenomena which deserve further investigations.In the study of hadronic matter at finite temperature and density,we propose a method for calculating the equation of state(EOS)of QCD at finite temperature and density.We find that the quark number density is fully determined by the quark prop-agator.Subsequently,the pressure density is composed of two parts:a constant term independent of ? but dependent on T and a ?,T-dependent term determined totally by the quark propagator.All these study will provide effective approaches to further s-tudies of phase structure and phase transition in QCD at finite temperature and density,astrophysics and cosmology.In the thesis,we calculate the equation of state(EOS)of QCD at finite chemical potential and zero temperature in the framework of a nonper-turbative propagator model.We find that the critical chemical potentials of the quark number density and the pressure density depend on the pole distribution of the quark propagator.When the chemical potential is smaller than the critical value,the pressure density and the pressure density vanish.By studying the linear response of the dressed quark propagator to an external background field,and based on QCD sum rule,we obtain a model-independent and rigorous formula for the vacuum susceptibility.The quark number susceptibility(QNS)is related to the phase transition from the confined/chirally broken phase to the de-confined/chirally restored phase and the quark number density is associated with the equation of state of QCD.In the thesis,we study the QNS at finite chemical potential and zero temperature and finite temperature.The results show that at zero temperature there is a critical chemical potential at which a first order chiral phase transition oc-curs.At finite temperature,there is also a chiral phase transition point at some critical temperature.Our results show that this point is neither a first order nor a second order phase transition point,perhaps a signal of a crossover.The studies on compact stars have attracted astronomers and physicists' attention for a long time,because it plays a very important role in our understanding of the dy-namical evolution of the stars,the condition of matter,the development and verification of the fundamental physical theory.In the thesis,using our EOS and the energy density relation,we obtain the structure of quark and neutron stars by integrating the Tolman-Oppenheimer-Volkoff(TOV)equation.The obtained relations between the maximal mass radius and central density for the different values of B are found to be consistent with the recent astronomical observation.