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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 potential is represented by a selection of contemporary studies that focus on solving the Bethe-Salpeter equation, deriving an exact mass formula in QCD that describes light and heavy pseudoscalar mesons simultaneously, and the calculation of the electromagnetic pion form factor and the vector meson electroproduction cross sections. These applications emphasise the qualitative importance of the momentum-dependent dressing of elementary Schwinger functions in QCD, which provides a unifying connection between disparate phenomena. They provide a solid foundation for an extension of the approach to nonzero temperature and chemical potential. The essential, formal elements of this application are described and four contemporary studies employed to exemplify the method and its efficacy. They study the demarcation of the phase boundary for deconfinement and chiral symmetry restoration, the calculation 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 continuum order parameter for deconfinement is introduced, an anticorrelation between the response of masses and decay constants to T and their response to mu elucidated, and a (T,mu)-mirroring of the slow approach of bulk thermodynamic quantities to their ultrarelativistic limit highlighted. These effects too are tied to the momentum-dependent dressing of the elementary Schwinger functions.