Development of many-body perturbation theory

Abstract

The development of standard MBPT for single-reference and multi-reference cases is reviewed, and its extension to the relativistic case in the form of the Dirac–Coulomb–Breit (DCB) approximation is described. The latter scheme is non-covariant, and the recent development of a fully covariant MBPT scheme is discussed. This is based upon a new scheme for quantum-electrodynamical (QED) calculations, the covariant-evolution-operator method, which is combined with standard MBPT. This scheme is fully compatible with the relativistically covariant Bethe–Salpeter equation. Some numerical results of the new scheme are given.

Keywords:

• perturbation theory
• quantum-electrodynamics
• electron correlation
• relativistic covariance
• evolution operator

Acknowledgements

The author wants to thank his co-workers Sten Salomonson and Daniel Hedendahl for fruitful collaboration. This work has been supported by the Swedish Research Council (VR).

Notes

Notes

1. We use here natural or relativistic units: c = ħ = m _e = ε₀ = 1, e ² = 4πα, α being the fine-structure constant.

2. In the following we shall leave out the subscript ‘I’.