Quantum Fluctuations In Strongly Interacting Hot And Dense Matter

As an important part of the standard model, quantum chromodynamics describes thestrong interaction which is mediated by gluons. Diferent from the asymptotic freedomat a high-energy scale, the phase structure is very complicated at a low and intermediate-scale. Among these phases transitions the most interesting ones are deconfinement andchiral phase transition. For the color is confined in hadrons at low and intermediate-scale, efective models without color interaction are usually used to study the chiralphase transition. Meanwhile at this energy scale, because of the strong coupling con-stant，nonperturbative methods are required. In this thesis we study the phase structureof the strongly interacting matter in QCD efective models with the random phase ap-proximation and functional renormalization group. Besides, the self-consistent Hatreeapproximation is also introduced.With the random phase approximation, the quantum fluctuations above mean fieldare constructed in the NJL model at finite temperature and isospin chemical potential.By calculating the meson contribution to the static quark potential, the Goldstone mode,which corresponds to the isospion symmetry spontaneous breaking, controls the poten-tial. In the pion superfluid quarks are always strongly coupled by the Goldstone mode. Inorder to consider the thermal and quantum fluctuations more self-consistently, we adoptthe functional renormalization group method to study the UA(1) and chiral symmetries atfinite temperature in the linear sigma model. In the framework of the functional renor-malization group, symmetries can be easily respected and the correct critical behavior atphase transitions can be obtained. In this thesis, by guaranteeing the Nambu–Goldstonetheorem, the UA(1) and chiral symmetries are both restored as temperature increases. Asa result, the obtained meson spectrum agrees well with the symmetry restoration.