Propagators in Quantum Chemistry, 2nd Edition

Chapter 1

Introduction

This text has grown out of the monograph “Propagators in Quantum Chemistry” by J. Linderberg and Y. Öhrn, Academic Press, London, 1973, which has been out of print for some time. The content is revised to take into account some of the considerable literature in the intervening years by many workers in the field. However, this is not intended as a review of the theory and application of propagators, but rather an attempt to present the theory and the basic approximations in a unified manner with some illustrative applications. The material is presented from our own perspective, and we apologize for any omissions of references to important work in the field.

Propagators gained early prominence in formal many-body theory of fermion systems¹. Concerns about the elimination of unlinked terms in the perturbation expansions and the associated correct scaling with systems size naturally led to the propagator concept. Treatment of double-time Green’s functions (propagators)² established that they provide an important and useful link between pure state quantum mechanics at the absolute zero of temperature and quantum statistical mechanics employing ensembles at finite temperature. Condensed matter theory employed the propagator concept to great advantage³. Recent advances in computational techniques and power of electronic computers have led to numerous successful applications of approximate propagator theory for so-called quasiparticle calculations in solids ⁴. Propagator ...