The Complex Scalar Field In External Magnetism With OPT Method

Quark-gluon plasma is one of the frontiers in particle physics.It is an important component of QCD phase diagram.When temperature rises(or density rises),the phase transition from hadronic phase to QGP phase happens.The most common phase transitions are confinement-deconfinement phase transition and chiral transition,both are related to the spontaneous symmetry breaking of the theory.The reason is,the thermal motion of quarks and gluons in a hadron becomes stronger when temperature rises,or the boundary among different hadrons becomes obscure or even vanishes when the hadrons are under great pressure,in both cases,deconfinement phase transition will happen.While the order parameter of chiral phase transition is quark condensation,which will be broken by rising temperature,then chiral phase transition appears.In addition,color superconductivity is an important component of the QCD phase diagram too.The structure of the QCD phase diagram is very abundant.One of the reasons is that QCD have several important properties,such as the breaking of chiral symmetry,confinement and asymptotic freedom.The other is that the number of quark flavors,the mass of quarks and external magnetism will affect phase transitions,which aggravates the complexity further.Strong magnetism will be produced in high energy heavy ion collision,so it is necessary to take magnetism into account in investigating QCD phase transition.Indeed,one finds important consequences induced by external magnetism,for example,magnetic catalysis.Finite temperature QCD is the basic theory in studying hadronic matter.But similar to the zero temperature QCD,the confinement property of the strong interaction leads to serious difficulties.Furthermore,in the finite temperature case,temperature itself will also need more computing technology,that calculation becomes more complicated.Therefore as in the zero temperature case,the effective theory is still an important way.For example,the chiral perturbation theory,the linear ? model,the NJL model are widely applied in QCD phase transition studying.In this thesis we calculated the free energy and mass for the complex scalar field under uniform magnetic field by using OPT method.The OPT is essentially a variational method,which reorganize the Lagrangian of the system by introducing artificial mass parameter and expansion constant,then one performs series expanding and renormalization,in the end require the most insensitivity of physical quantities to fix artificial mass parameter,so that some of the nonperturbation effects are included.In this thesis,we calculate the free energy totwo loop order and take renormalization into account.Our result can be used to calculate other physical quantities such as entropy.