Perturbative Methods in Many-Body Problems

Philippe A. Martin, FRANÇOIS ROTHEN

Decio Levi B, O. Ragnisco

Manuel Valiente

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.

Reiner M. Dreizler, Eberhard K. U. Gross

BRUCE R. BARRETT

A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei.

Yoshio Kuramoto