Stability and instability of relativistic electrons in classical electromagnetic fields

Elliott H. Lieb, Heinz Siedentop, Jan Philip Solovej

Research output: Chapter in Book/Report/Conference proceedingChapter


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 languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages23
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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


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