Gravitational collapse in quantum mechanics with relativistic kinetic energy

Elliott H. Lieb, Walter E. Thirring

Research output: Contribution to journalArticle

64 Scopus citations

Abstract

It is proved that the quantum mechanical Hamiltonian H = Σi=1N (p2 + m2) 1 2 - κ Σi>j|xi - xj|-1 for bosons (resp, fermions) is bounded from below if N ≤ cbκ-1 (resp. N ≤ cfκ -3 2). H is unbounded from below if N ≥ cblκ-1 (resp. N ≥ cflκ -3 2). The constants cb and cbl (resp. cf and cfl) differ by about a factor 2 (resp. 4).

Original languageEnglish (US)
Pages (from-to)494-512
Number of pages19
JournalAnnals of Physics
Volume155
Issue number2
DOIs
StatePublished - Jan 1 1984

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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