Stability of relativistic matter with magnetic fields

Elliott H. Lieb, Heinz Siedentop, Jan Philip Solovej

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Stability of matter with Coulomb forces has been proved for nonrelativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic fields. In both cases stability requires that the fine structure constant α be not too large. It was unclear what would happen for both relativistic dynamics and magnetic fields, or even how to formulate the problem clearly. We show that the use of the Dirac operator allows both effects, provided the filled negative energy “sea” is defined properly. The use of the free Dirac operator to define the negative levels leads to catastrophe for any α, but the use of the Dirac operator with magnetic field leads to stability.

Original languageEnglish (US)
Pages (from-to)1785-1788
Number of pages4
JournalPhysical review letters
Issue number10
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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