The Complex Scalar Field At Finite Temperature And Chemical Potential

The properties of strongly-interacting matter at nonvanishing temperature and/or density are hotly discussing topics in particle physics.One supposes that the phase diagram of quantum chromodynamics(QCD)has very abundant contents,for example the hadronic phase,the quark gluon plasma(QGP)phase and various color superconducting phases.The phase structure of QCD is important not only for our understanding QCD but also for investigating the early evolution of our universe.Moreover,they can be realized in heavy-ion experiments as well as some stars.Indeed,heavy-ion experiments aiming at probing the phase structure of QCD at various facilities such as GSI,JINR,CERN and BNL are on progress.Sufficiently high magnetic fields is currently being generated in these experiments with a nonzero impact parameter.Therefore the effect of magnetic fields should be taken into account.At vanishing density,lattice simulations based on the first principle provide additional insights that are complementary to experimental studies.They are important reference especially when experimental information is scarce.However,at nonvanishing chemical potential,lattice simulations confronted serious difficulties resulting from the sign problem.Although impressive progress has been made to overcome this problem,lattice simulations are still restricted to small chemical potential.Since resolving strong coupling QCD is very difficult and many effective models have been employed successfully in zero temperature situation,effective models become also an important tool for investigating properties of strongly-interacting matter at nonzero temperature and/or chemical potential.Two of extensively applied low-energy effective models are the Nambu-Jona-Lasinio(NJL)model and quark-meson(QM)models,which can describe the chiral dynamics of QCD;their Polyakov-loop extended versions have advanced our understanding of the confinement-deconfinement aspects of the QCD phase structure.It is well-known that calculating thermal quantites is a tough task.Multiple scales result in complexity in perturbation.For example at high temperatures,powers of coupling constants can become surmounted by powers of the temperature.Thus high temperature field theories in essential are nonperturbative.To realize nonperturbative calculation,ring diagram schemes,two-particle irreducible(2PI)effective actions,hard-thermal-loop resummation,variational methods,like the screened perturbation theory and the optimized perturbation theory(OPT)are used.In this thesis we investigate the complex scalar field in magnetic background at finite temperature and chemical potential by using OPT method.We calculate the temperature behaviors of the grand potential with the same strength of a magnetic field and different chemical potentials as well as the same chemical potential and different strength of a magnetic field.The results show that the grand potential,(a)decreases with increasing temperature,(b)is sensitive to and increases with increasing strength of the magnetic field,(c)is not so sensitive to the chemical potential and decreases when the chemical increases.