Stability of Matter

  • Walter Thirring
Part of the NATO ASI Series book series (NSSB, volume 144)


Matter around us consists of electrons and nuclei and the laws of nature which govern their behaviour are well-known. The Coulomb force is dominant except for cosmic bodies where gravity takes over. Quantum mechanics is essential for the structure of matter. Thus the Hamiltonian
$$H = \sum\limits_{i = 1}^N {\frac{{P_i^2}}{{2{m_i}}}} + \sum\limits_{i > j} {\frac{{{e_i}{e_j} - \kappa {m_i}{m_j}}}{{|{x_i} - {x_j}|}}}$$
which contains these two forces should express, when treated quantum mechanically, the main features of atoms, molecules, macroscopic and cosmic bodies. (1) is not a fundamental law of nature but what is fundamental is an ever retreating fata morgana which leaves behind in its wake approximate laws like (1) which describe the gross features of a large number of phenomena. Although (1) is too complex to allow all curious properties of odd substances to be deduced by fair mathematical means it is gratifying that the important properties common to all forms of matter can be derived from (1) flawlessly. In this way mathematical physics could unravel deeper connections between the laws of quantum theory and thermodynamics. Conclusive deductions require necessarily some greater mathematical effort but fortunately the results are sufficiently transparent so that one can understand them by simple heuristic considerations. This will be done in sections 2 and 3 where we will try to guess what happen for temperature T=0 and for T>0.


Thermodynamic Stability Coulomb Force Effective Field Theory Convex Envelope Deep Connection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E.H. Lieb, W. Thirring, Phys. Rev. Lett. 35, 687 (1975).ADSCrossRefGoogle Scholar
  2. 2.
    I. Daubechies, Commun. Math. Phys. 90, 511 (1983).MathSciNetADSCrossRefMATHGoogle Scholar
  3. 3.
    E.H. Lieb, S. Oxford, Int. J. Quantum Chem. 19, 427 (1981).CrossRefGoogle Scholar
  4. 4.
    E.H. Lieb, B. Simon, Adv. Math. 23, 22 (1977).MathSciNetCrossRefGoogle Scholar
  5. 5b.
    F.J. Dyson, A. Lenard, J. Math. Phys. 8, 423 (1967)MathSciNetADSCrossRefMATHGoogle Scholar
  6. 5a.
  7. 6.
    E.H. Lieb, Phys. Lett. 70, 71 (1979).MathSciNetCrossRefGoogle Scholar
  8. 7.
    J.M. Levy-Leblond, J. Math. Phys. 10, 806 (1969).ADSCrossRefGoogle Scholar
  9. 8.
    P. Hertel, W. Thirring, in: “Quanten und Felder”, ed. H. Dürr, Vieweg (1971).Google Scholar
  10. 9.
    E.H. Lieb, W. Thirring, Ann. of Phys. 155, 494 (1984).MathSciNetADSCrossRefGoogle Scholar
  11. 10.
    J. Conlon, Commun. Math. Phys. 94, 439 (1984).MathSciNetADSCrossRefGoogle Scholar
  12. 11.
    P. Landsberg, J. Stat. Phys. 35, 159 (1984).MathSciNetADSCrossRefGoogle Scholar
  13. 12.
    J. Lebowitz, E.H. Lieb, Adv. Math. 9, 316 (1972).MathSciNetCrossRefGoogle Scholar
  14. 13.
    P. Hertel, H. Narnhofer, W. Thirring, Commun. Math. Phys. 28, 159 (1972).MathSciNetADSCrossRefGoogle Scholar
  15. 14a.
    A. Pflug, Commun. Math. Phys. 78, 83 (1980);MathSciNetADSCrossRefGoogle Scholar
  16. 14b.
    A. Pflug J. Messer, J. Math. Phys. 22, 2910 (1981).Google Scholar

Review Articles

  1. E.H. Lieb, Rev. Mod. Phys. 48, 553 (1976).MathSciNetADSCrossRefGoogle Scholar
  2. W.E. Thirring, A Course in Mathematical Physics, Vol. IV, Springer, Wien-New York (1983).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Walter Thirring
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria

Personalised recommendations