Many-body theory

In the theoretical solid state physics, many-body theory (English many- body theory ) is the quantum mechanical description of a very large number of interacting microparticles ( bosons, fermions ) and their collective behavior.

Such a system differs in its physical properties substantially from an isolated ( free ) particles. The fundamental problem is not in the number of participating particles, but in regard to their interaction.

The many-body theory considered in contrast to the many-body problem of classical mechanics and quantum effects and uses methods of quantum field theory. Their transfer to problems of solid state physics in the 1950s (David Pines, Philippe Nozières, Alexei Alexeyevich Abrikossow, Lev Landau, Arkady Migdal, David Bohm, Murray Gell-Mann, Julian Schwinger, Joaquin Mazdak Luttinger, etc.) led to the emergence of many-body theory.

Because, among other things with it not only solids ( metals, semiconductors, dielectrics, magnetism, etc.), but also liquids, superfluids, superconductors, plasmas be treated so matter in all possible phases, this development also stands for the transition from the theoretical solid state physics to the physics of condensed matter.

A possible physical description is done by

• Elementary excitations or quasiparticles,
• Canonical transformation as in the reduction of the problem of an effective one-body problem Kepler,
• The aid of quantum statistics, the self-energy -functional theory,
• Methods of quantum field theory such as the so -called second quantization, the Green's functions and the perturbative description with the help of Feynman diagrams.