### Abstract

Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfies E_{0}≦-AN^{7/5}. We prove that 7/5 is the correct power by proving that E_{0}≧-BN^{7/5}. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed that E_{0}≦-CNρ^{1/4}. This 1/4 law is also validated here by showing that E_{0}≧-DNρ^{1/4}. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.

Original language | English (US) |
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Pages (from-to) | 417-448 |

Number of pages | 32 |

Journal | Communications in Mathematical Physics |

Volume | 116 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1988 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

Conlon, J. G., Lieb, E. H., & Yau, H. T. (1988). The N7/5 law for charged bosons.

*Communications in Mathematical Physics*,*116*(3), 417-448. https://doi.org/10.1007/BF01229202