Nonperturbative effects in QCD at finite temperature and density

These lecture notes illustrate the application of Dyson-Schwinger equations in QCD. The extensive body of work at zero temperature and chemical potent ial is represented by a selection of contemporary studies that focus on sol ving the Bethe-Salpeter equation, deriving an exact mass formula in QCD tha t describes light and heavy pseudoscalar mesons simultaneously, and the cal culation of the electromagnetic pion form factor and the vector-meson elect roproduction cross sections. These applications emphasize the qualitative i mportance of the momentum-dependent dressing of elementary Schwinger functi ons in QCD, which provides a unifying connection between disparate phenomen a. They provide a solid foundation for an extension of the approach to nonz ero temperature and chemical potential. The essential, formal elements of t his application are described, and four contemporary studies are employed t o exemplify the method and its efficacy. They study the demarcation of the phase boundary for deconfinement and chiral symmetry restoration, the calcu lation of bulk thermodynamic properties of the quark-gluon plasma, and the response of pi- and rho- meson observables to T and mu. Along the way a con tinuum order parameter for deconfinement is introduced, an anticorrelation between the response of masses and decay constants to T and their response to mis elucidated, and a (T, mu) mirroring of the slow approach of bulk the rmodynamic quantities to their ultrarelativistic limit is highlighted. Thes e effects too are tied to the momentum-dependent dressing of the elementary Schwinger functions. (C) 1999 American Institute of Physics. [S1063-7796(9 9)00103-5].