## Abstract

There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G(0)W(0) approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated.

Original language | English |
---|---|

Article number | 235106 |

Pages (from-to) | - |

Number of pages | 6 |

Journal | Physical Review B |

Volume | 64 |

Issue number | 23 |

DOIs | |

Publication status | Published - 15 Dec 2001 |

### Bibliographical note

© 2001 American Physical Society. Published in Physical Review B and uploaded in accordance with the publisher's self archiving policy.## Keywords

- SPACE-TIME METHOD
- ELECTRON-GAS
- SPECTRAL FUNCTIONS
- GW APPROXIMATION
- BAND-GAPS
- SEMICONDUCTORS
- SURFACE
- DENSITY
- CONSERVATION
- INSULATORS