Hadrons in Vacuum and Matter

In the first part of this thesis, we investigate the correlators and form factors of hadrons in vacuum viewed as a dilute gas of instantons and antiinstantons. Relying heavily on approximate bosonization techniques in four dimensions, we construct an effective action for constituent quarks in interaction with mesons and glueballs. The effective action is then used to study various meson, baryon and glueball point-to-point correlation functions. Using the rationale of QCD in the large number of color limit, the hadronic correlators are explicitly calculated in momentum space and then Fourier transformed to configuration space. The results are compared to recent simulations using instantons and cooled lattice gauge theories. They compare favourably in the simulated range of 0 - 1.5 fm, despite the fact that some important channels such as the rho or isobar, lack the pertinent singularities in momentum space, and that the vacuum state may be unstable (occurrence of tachyonic modes). An estimate of the quark condensate is obtained. We derive and comment on a variety of quark and nucleon form factors. An extended bosonization procedure accounting for quark-glueball coupling is introduced and discussed. This work provides a powerful alternative to expensive simulations. In the second part of this thesis, we discuss the role of temperature on hadronic states. We use the nucleon as a primary example, although our arguments extend to all hadrons. At finite temperature the concepts of masses, charges and widths are argued to be process dependent. For instance the nucleon mass-shift can be inferred either from its energy or its correlation functions. Using Ward identities we derive exact relations for the mass-shift of the nucleon following from its pole mass (time-like correlation function). At low temperature the shift is real, negative and driven by the pion-nucleon S-wave scattering length. Since the nucleon may be viewed as a soliton, we investigate these issues in details using two-dimensional models where some exact results are derived. A qualitative analysis of the Skyrmion at finite temperature and to one -loop is also discussed.