Hadron-quark matter phase transition

This is a lecture note concerning the phase transition between a hadron matter and a quark matter. The Gibbs energy, the phase diagram and the heating curve by heavy ion collision are explained at first. The theory of a field at finite temperature is described. A many body system can be treated thermodynamically. The models of hadron-quark matter phase transition are presented, and those are statistical bootstrap model, average field model to evaluate free energy, perturbative QCD, bagged QCD, and the lattice gauge theory by using Monte Carlo calculation. The mechanism of phase transition and the observation are discussed. The statistical quark bag model developed by the author and others is presented. This model can discuss negative surface energy, hadron-multi quark bag-quark, gluon, plasma phase transition, and large transverse momentum and quark matter formation. It can be concluded that a hadron matter makes the phase transition to a quark matter when high temperature and high density state is kept sufficiently long. The estimated energy of the production of quark-gluon-plasma by heavy ion collision was 5-50 GeV/nucleon. (Kato, T.)