On Debye Screening Mass In Hot And Dense QED And The Specific Heat Of Color-Superconducting Matter

High energy hadron collision is a very important field in present physics and the research of QGP physics is very significant, which can be summarized as three accepts, one is to explore the new matter on quark, second is to further confirm dynamics on quark and develop pertinent thermodynamics through researching collective behavior of one system. The third is helpful for people to analyze and explore the unknown things in our universe, such as the evolvement of early universe, the inner structure of neutron stars, the non-conservation of baryons and unclear matter in the university, and so on. QGP is an exploring matter,which comes from hadron matters through deconfinement phase transition. If the existence of QGP is confirmed, not only people will know a new matter, but also a great improvement in the basic physical conception will come. The research of QGP is a very important field in the present physics.QCD at finite temperature is the theory to do research about QGP. In the middle of 1970's, it is quantum field theory at finite temperature that predicts the existence of QGP. Quantum field theory at finite temperature is a statistical thermodynamic theory in field. It offers one of the most convenient framework, to deal with a large number of par-ticles,which is often referred to as the 'Many -Body Problem. And it has been widely applied into other main physical problems,such as color superconductivity.The Debye mass is a very important physical parameter which describes the collective motion of a hot and /or dense plasma. Electricallycharged particles in this plasma react to electromagnetic fields and cause screening of static electric fields at large distance. The inverse screening length is called Debye mass. There have been many works about it. But they were all resulted by direct calculation of the self-energy and the gauge fields. The approach could be very complicated, especially when dealing with two or higher loop self-energy diagrams. Here we adopt an alternative method. The specific of color superconducting matters is also a very important physical parameter, which describes the thermo-dynamical property of matters. There have been many works about it, here we adopt a simple method to calculate the specific of quark without calculating the contribution of gloun. The thesis is divided into three parts. The first part is a brief review of Finite-Temperature Field Theory. In the second part staring from the Schwinger-Dyson equation for the photon propagator in QED in the theory frame of Finite-Temperature Field Theory, we derive a useful relation between the Debye mass and thermodynamic pressure. Using this relation, we calculate the two-loop Debye mass from relevant pressures at finite temperature and chemical potential. The result indicates that the two-loop correction decrease the Debye screening mass. We also discuss the magnetic mass in QED plasma. In the third part we introduce the basic theory and its application to color superconductivity, then we calculate the specific heat of Color-Superconducting matter-quark from Hamiltonian.