Perturbative Studies On The Thermoldynamics Of Quark-gluon Plasm

One of the most important goals in high energy nuclear physics is to explore a new form of matter which is the so-called Quark Gluon Plasma(QGP).To study the equation of state of QGP,at the asymptotically high temperature,one could perturba-tively calculate the thermodynamics from first principles.On the other hand,close the critical temperature,it is often necessary to construct phenomenological models based on the lattice Quantum Chromodynamics(QCD)simulations among which the matrix models for deconfinement can well describe the physical behavior of QGP near the phase transition point.The basic structure of matrix models depends on the perturba-tive contributions of the thermal effective potential in a background field.Therefore,by computing higher order perturbative corrections,we could systematically improve the thermodynamics at high temperatures and analyze all the possible forms of the non-prturbative contributions for these models.In the framework of quantum field theory at finite temperature,we calculate the two-loop effective potential in a background field by utilizing the technique of Feynman diagram expansion.In pure gauge theories,there is a simple proportional relation between the leading order effective potential and its two-loop correction which is independent on the background fields.Our results show that the inclusion of fermions leads to the violation of such a proportional relation.In addition,with the temperature dependence of the background fields determined by matrix models,we numerically study the effects of the background fields on the thermodynamics of QGP,as well as the dependence of such effects on the fermions' mass and chemical potential.Under certain limit conditions,we expand the effective potential in a background field and obtain a series of analytical expressions which could be important for theoretical studies on the equation of state of QGP.