Abstract
The analysis of the ground state energy of Coulomb systems interacting with magnetic fields, begun in Part I, is extended here to two cases. Case A: The many electron atom; Case B: One electron with arbitrarily many nuclei. As in Part I we prove that stability occurs ifzα12/7<const (in case A) andzα2<const (in case B), (z∣e∣=nuclear charge, α=fine structure constant), but a new feature enters in case B. There onealso requires α<const, regardless of the value ofz.
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Fröhlich, J., Lieb, E.H., Loss, M.: Stability of Coulomb systems with magnetic fields. I. The one-electron atom. Commun. Math. Phys.104, 251–270 (1986)
Daubechies, I., Lieb, E.H.: One electron relativistic molecules with Coulomb interaction. Commun. Math. Phys.90, 497–510 (1983)
Conlon, J.: The ground state energy of a classical gas. Commun. Math. Phys.94, 439–458 (1984)
Fefferman, C., de la Llave, R.: Relativistic stability of matter I. Revista Iberoamericana (to appear)
Ni, G., Wang, Y.: Vacuum instability and the critical of the coupling parameter in scalar QED. Phys. Rev. D27, 969–975 (1983)
Finger, J., Horn, D., Mandula, J.E.: Quark condensation in quantum chromodynamics. Phys. Rev. D20, 3253–3272 (1979)
Lieb, E.H., Thirring, W.: Bound for the Kinetic energy of fermions which proves the stability of matter. Phys. Rev. Lett.35, 687 (1975). Errata35, 1116 (1975)
Avron, J., Herbst, I., Simon, B.: Schrödinger operators with magnetic fields. I. General interactions. Duke Math. J.45, 874–883 (1978)
Lieb, E.H., Thirring, W.: Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. In: Studies in Mathematical Physics, Essays in honor of Valentine Bargmann, Lieb, E.H., Simon, B., Wightman, A.S. (eds.). Princeton, NJ: Princeton University Press 1976
Lieb, E.H.: On characteristic exponents in turbulence. Commun. Math. Phys.92, 473–480 (1984)
Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979
Lieb, E.H.: The number of bound states of one-body Schrödinger operators and the Weyl problem. Proc. Am. Math. Soc. Symp. Pure Math.36, 241–252 (1980)
Loss, M., Yau, H.-T.: Stability of Coulomb systems with magnetic fields. III. Zero energy bound states of the Pauli operator. Commun. Math. Phys.104, 283–290 (1986)
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Communicated by A. Jaffe
Work partially supported by U.S. National Science Foundation grant PHY-8116101-A03
Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858.
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Lieb, E.H., Loss, M. Stability of Coulomb systems with magnetic fields. Commun.Math. Phys. 104, 271–282 (1986). https://doi.org/10.1007/BF01211594
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DOI: https://doi.org/10.1007/BF01211594