The stability and instability of relativistic matter

Elliott H. Lieb, Horng Tzer Yau

Research output: Chapter in Book/Report/Conference proceedingChapter


We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namely p2/2m is replaced by (p2 c 2 + m2 c4)1/2 - mc2. The electrons are allowed to have q spin states (q = 2 in nature). For one electron and one nucleus instability occurs if zα > 2/π, where z is the nuclear charge and α is the fine structure constant. We prove that stability occurs in the many-body case if zα 2/π and α < 1/(47q). For small z, a better bound on α is also given. In the other direction we show that there is a critical αc (no greater than 128/15π) such that if α > αc then instability always occurs for all positive z (not necessarily integral) when the number of nuclei is large enough. Several other results of a technical nature are also given such as localization estimates and bounds for the relativistic kinetic energy.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages37
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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