### Abstract

The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary classical magnetic field of finite energy. Despite the previously known facts that ordinary nonrelativistic matter with magnetic fields, or relativistic matter without magnetic fields, is already unstable when α, the fine structure constant, is too large, it is noteworthy that the combination of the two is still stable provided the projection onto the positive energy states of the Dirac operator, which defines the electron, is chosen properly. A good choice is to include the magnetic field in the definition. A bad choice, which always leads to instability, is the usual one in which the positive energy states are defined by the free Dirac operator. Both assertions are proved here.

Original language | English (US) |
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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 535-557 |

Number of pages | 23 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Keywords

- Dirac operator
- Instability of matter
- Magnetic fields
- Relativistic
- Schrödinger operators
- Stability of matter

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## Cite this

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 535-557). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_36