Comparison of Heisenberg’s New Tamm-Dancoff Method with Approximation Schemes used in Many-Body Theory

Abstract

In the theoretical investigation of nonrelativistic feimion systems, several characteristic approximation schemes play a decisive role. Examples are the BCS theory of superconductivity, the Hartree-Fock method in atomic and molecular physics and its generalization by means of the Bogoliubov theory (containing also BCS as a special case) used in nuclear physics. Furthermore, the Random-Phase-Approximation (RPA) is of fundamental importance in plasma physics as well as in the explanation of the well known vibrational states of nuclei. In this connection, it should be pointed out that the socälled nuclear models, which to a certain extent brought nuclear physics into miscredit, represent in fact nothing else but a more or less intuitive substitute for special well defined approximation schemes: the introduction of an average potential in heavy nuclei stands for Hartree-Fock, whereas the so-called surface vibrations visualize RPA. In addition, the possibility to describe elementary excitations by the naive concept of independent particle motion is justified theoretically by the Bogoliubov transformation which leads to the so-called quasi-particles.