Renormalised perturbation theory of normal systems

Lambert, Colin and Hagston, W. E. (1981) Renormalised perturbation theory of normal systems. Journal of Physics A: Mathematical and General, 14 (7). pp. 1533-1542. ISSN 0305-4470

Abstract

Employing an infinite hierarchy of equations for the Green functions of a many particle system in its ground state mod psi N), the well known non-relativistic, time-dependent, ground-state perturbation theory of a normal system of interacting fermions is derived, without introducing the hypothesis that mod psi N) is the adiabatic transform of a non-interacting state. This new formulation of the problem allows us to renormalise conventional perturbation theory by introducing an effective interaction Gamma and the final result is a highly summed and manifestly self-consistent perturbation expansion in powers of Gamma . The authors calculate Gamma to second order and demonstrate that many of the well known results of time-dependent perturbation theory may be obtained by choosing the simplest approximations for Gamma . The results are readily generalised to finite temperatures and the formalism provides a generalised form of Hartree-Fock theory which may have important applications in many areas of physics.