Many-Body Perturbation Theory

Abstract

The second quantized formalism is perhaps most extensively utilized in the field of perturbation theory of many-electron systems. This is due to the tedious derivations necessary to arrive at feasible working formulae, especially at the higher orders of PT. This topic has a quite rich literature, including books (Raimes 1972, Mattuck 1976, Jørgensen & Simons 1981, Szabó & Ostlund 1982, Wilson 1984, 1987), reviews (Paldus & Cižek 1975) as well as timely scientific papers (see, e.g. Kutzelnigg 1984, Urban et al. 1984, Saebo and Pulay 1988, Cullen 1988, Kapuy et al., 1987) the latter indicating that this field is being actively cultivated. In the spirit of the present treatment, we shall not address the most advanced problems of many-body perturbation theory (MBPT). Rather, the forthcoming chapter offers a simple introduction permitting one to pick up the basis ideas of MBPT. In particular, we shall derive the second-order Møller-Plesset formula for the correlation energy.