10 Chapter 1: Introduction the low energy side, Lee and Wick showed that scalar field theories could support an ‘abnormal’ nuclear state with properties far different from those in the usual vacuum [68]. In more modern language there is a nonzero vacuum expectation value for a quark condensate which one expects to melt at higher temperatures, thus restoring chiral symmetry. Both the statistical model of Hagedorn [69, 70] and the hadronic mean field approach of Walecka [71–73] predict a phase transition; see Fig. 1.5. From the QCD side, and before the advent of asymptotic freedom, Itoh was the first to suggest the possibility of deconfined quark matter [74], followed by Carruthers (as cited in [67]). Collins and Perry [75] were the first to recognize the importance of asymptotic freedom, leading at large energies to a ‘quark soup.’ Shuryak coined the name ‘quark-gluon plasma’ (QGP) [76] as noted in [77]. The characteristic length for the polarization of the medium caused by color charges is the inverse of the Debye mass, µ$_{D}$ ∼ gT , which is related to the temperature of the plasma. LQCD calculations of the static q ¯ q potential as a function of distance and temperature show that for T > T$_{c}$ the potential is screened; see Fig. 1.6 (a). Lattice calculations show a sharp rise of entropy density as a function of temperature, with the density afterward given by an ideal gas with quark and gluon degrees of freedom to within 20%; recent results using almost physical quark masses [78] are shown in Fig. 1.6 (b). There is disagreement within the lattice community as to whether the chiral transition and the deconfinement transition occur simultaneously. Nevertheless all these