Many-body methods at finite temperature

The approximation methods relevant to describe many-fermion systems at finite temperatures are reviewed. The grand canonical formalism is outlined for independent fermions, and its applicability to the case of finite nuclei is discussed for which fluctuations arising from the small number of particles involved are expected to be sizeable. Derivation of the mean field equations is presented based on the variational method. Perturbation expansions of partition functions are discussed. A particularly important subseries containing the so called ring diagrams whose summation leads to the random phase approximation (RPA) is studied. An application to the physics of giant resonances in hot nuclei is described. (K.A.) 64 refs., 3 figs