Standard many-body methods
The correlations and responses of a many-particle system are sufficiently important that a great deal of formalism has been developed to compute them. In many cases of experimental interest, however, simply calculating perturbation theory of some response has not been very helpful, and a fresh non-perturbative insight was required, as in BCS theory or the fractional quantum Hall effect. Perhaps a more immediate use of the formalism we develop, sometimes informally called "Green's functions", is to understand what experiments actually measure in a many-particle system. Since measuring the full wave function is impossible for a thermodynamical number of particles, real experiments typically measure some low-order correlation function, and understanding the different types of correlation functions that experiments measure is an important aspect of the current material.