The stability and instability of relativistic matter |
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Authors: | Elliott H Lieb Horng-Tzer Yau |
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Institution: | (1) Departments of Mathematics and Physics, Princeton University, P.O. Box 708, 08544 Princeton, NJ, USA;(2) School of Mathematics, The Institute for Advanced Study, 08540 Princeton, NJ, USA |
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Abstract: | 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, namelyp
2/2m is replaced by (p
2
c
2+m
2
c
4)1/2–mc
2. The electrons are allowed to haveq spin states (q=2 in nature). For one electron and one nucleus instability occurs ifz >2/ , wherez is the nuclear charge and is the fine structure constant. We prove that stability occurs in the many-body case ifz![agr](/content/h570323824181807/xxlarge945.gif) 2/ and <1/(47q). For smallz, a better bound on is also given. In the other direction we show that there is a critical
c
(no greater than 128/15 ) such that if >
c
then instability always occurs forall positivez (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.Work partially supported by U.S. National Science Foundation grant PHY-85-15288-A02The author thanks the Institute for Advanced Study for its hospitality and the U.S. National Science Foundation for support under grant DMS-8601978 |
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Keywords: | |
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