This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory. Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson systems.
Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field theoretic formulation of "bosonization" is presented; it is published here for the first time....

In interaction the between the leads to a quantum liquids particles variety of and unusual states of condensed matter interesting systems, super e.g. and the fractional in electron Hall effect conductivity quantum (FQHE) sys tems. In this book for we investigate quantum field theoretical approaches fermion the is interacting systems. Originally, quantum fieldtheory designed describe as a to perturbation theory weakly interacting many particle sys tems. For treatment of interaction and correlation effects a proper beyond the the series of must beresummed perturbation theory, Feynmandiagrams...