The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field: I. The lower bound

Communications in Mathematical Physics

Volumn 258, Issue 3, 2005, Pages 675-695

  Lieb, Elliott H ^a   Loss, Michael ^b  

^a PRINCETON UNIVERSITY   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22944453673     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1365-y     Document Type: Article

References (24)

1. Birman, M.Sh., Solomjak, M.: Spectral asymptotics of nonsmooth elliptic operators. II. Trans. Moscow Math. Soc. 28, 1-32 (1975). Translation of Trudy Moskov. Mat. Obv.
2. Bugliaro, L., Fröhlich, J., Graf, G.M.: Stability of quantum electrodynamics with nonrelativistic matter. Phys.Rev. Lett. 77, 3494-3497 (1996)
3. Dyson, F., Lenard, A.: Stability of Matter I. and II. J. Math. Phys. 8, 423-434 (1967)
4. and J. Math. Phys. 9, 698-711 (1968)
5. Fefferman, C., Fröhlich, J., Graf, G.M.: Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field. Proc. Natl. Acad. Sci. USA 93, 15009-15011 (1996);
6. Stability of ultraviolet cutoff quantum electrodynamics with non-relativistic matter. Commun. Math. Phys. 190, 309-330 (1997)
7. Fröhlich, J., Lieb, E.H., Loss, M.: Stability of Coulomb Systems with Magnetic Fields 1. The One-Electron Atom. Commun. Math. Phys. 104, 251-270 (1986)
8. Glimm, J., Jaffe, A.: Quantum field theory models. In: Statistical Mechanics and Quantum Field Theory, De Witt, C., Stora, R. (eds.), NY: Gordon and Breach, 1971
9. Lieb, E.H.: On Characteristic Exponents in Turbulence. Commun. Math. Phys. 92, 473-480 (1984)
10. Lieb, E.H.: The stability of matter and quantum electrodynamics. In: Proceedings of the Heisenberg symposium, Munich, Dec. 2001, Fundamental Physics-Heisenberg and Beyond, Buschhorn, G., Wess, J. (eds.) Berlin-Heidelberg-New York: Springer, 2004, pp. 53-68 (see Sec. 3);
11. A modified version appears in Milan J. Math. 71, 199-217 (2003).
12. A further modification appears in the Jahresbericht of the German Math. Soc. JB 106, 93-110 (Teubner)
13. Lieb, E.H.: Proofs of Some Conjectures on Permanents. J. of Math. and Mech. 16, 127-139 (1966)
14. Lieb, E.H., Lebowitz, J.L.: The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Adv. in Math. 9, 316-398 (1972)
15. Lieb, E.H., Loss, M.: A note on polarization vectors in quantum electrodynamics. Commun. Math. Phys. 252, 477-483 (2004)
16. Lieb, E.H., Loss, M.: A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics. J. Stat. Phys. 108, 1057-1069 (2002)
17. Lieb, E. H., Loss, M.: Self-Energy of Electrons in Non-perturbative QED. In: Differential Equations and Mathematical. Physics, University of Alabama, Birmingham, 1999, Weikard, R., Weinstein, G. (eds.) Providence, RI: Amer. Math. Soc./Internat. Press, 2000, pp. 255-269.
18. (A few errors have been corrected in the version in the book: Thirring, W. (ed.) The Stability of Matter: From Atoms to Stars, Selecta of E. H. Lieb, third edition, Berlin-Heidelberg-New York: Springer, 2001.)
19. Planck, M.: Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum. Verhandlung der Deutschen Physikalischen Gesellschaft 2, 237-245 (1900)
20. Lieb, E.H., Loss, M., Siedentop, H.: Stability of Relativistic Matter via Thomas-Fermi Theory. Helv. Phys. Acta 69, 974-984 (1996)
21. Lieb, E.H., Loss, M., Solovej, J-P.: Stability of matter in magnetic fields. Phys. Rev. Lett. 75, 985-989 (1995)
22. Lieb, E.H., Yau, H.T.: The Stability and Instability of Relativistic Matter. Commun. Math. Phys. 118, 177-213 (1988)
23. Loss, M.: Stability of matter in magnetic fields. In: Proceedings of the XII-th International. Congress of Mathematical Physics 1997, De Wit et al, (eds.), Cambridge: International Press, 1999, pp. 98-106
24. Weinberg, S.: The Quantum Theory of Fields: Volume I Foundations. Cambridge: Cambridge University Press, 1995