Gravitational collapse in quantum mechanics with relativistic kinetic energy

Elliott H. Lieb; Walter E. Thirring

doi:10.1016/0003-4916(84)90010-1

Gravitational collapse in quantum mechanics with relativistic kinetic energy

Elliott H. Lieb, Walter E. Thirring

Mathematics

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82 Scopus citations

Abstract

It is proved that the quantum mechanical Hamiltonian H = Σ_i=1^N (p² + m²)^{1 2} - κ Σ_i>j|x_i - x_j|^-1 for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^-1 (resp. N ≤ c_fκ^{-3 2}). H is unbounded from below if N ≥ c_b^lκ^-1 (resp. N ≥ c_f^lκ^{-3 2}). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).

Original language	English (US)
Pages (from-to)	494-512
Number of pages	19
Journal	Annals of Physics
Volume	155
Issue number	2
DOIs	https://doi.org/10.1016/0003-4916(84)90010-1
State	Published - Jul 1984

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1016/0003-4916(84)90010-1

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title = "Gravitational collapse in quantum mechanics with relativistic kinetic energy",

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).",

author = "Lieb, {Elliott H.} and Thirring, {Walter E.}",

year = "1984",

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doi = "10.1016/0003-4916(84)90010-1",

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T1 - Gravitational collapse in quantum mechanics with relativistic kinetic energy

AU - Lieb, Elliott H.

AU - Thirring, Walter E.

PY - 1984/7

Y1 - 1984/7

N2 - 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).

AB - 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).

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U2 - 10.1016/0003-4916(84)90010-1

DO - 10.1016/0003-4916(84)90010-1

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VL - 155

SP - 494

EP - 512

JO - Annals of Physics

JF - Annals of Physics

IS - 2

ER -

Gravitational collapse in quantum mechanics with relativistic kinetic energy

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