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How to Implement Boltzmann’s Probabilistic Ideas in a Relativistic World?

  • Michael K.-H. Kiessling
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 574)

Abstract

This article outlines some of the problems, as well as some recent progress, in the implementation of Boltzmann’s probabilistic ideas in a world ruled by relativistic gravity and electromagnetism.

Keywords

Black Hole Black Hole Thermodynamic Bohmian Mechanic Newtonian Gravity Relativistic World 
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.

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References

  1. 1.
    M. Abraham, Ann. Phys. 10, 105 (1903)Google Scholar
  2. 2.
    V.A. Antonov, Vest. Leningrad Gas. Univ. 7, 135 (1962) (English transl.: ‘Most probable phase distribution in spherical star systems and conditions for its existence.’ In: Dynamics of Star Clusters, ed. by J. Goodman and P. Hut, IAU 1985), pp. 525-540)Google Scholar
  3. 3.
    W. Appel, M. K.-H. Kiessling, ‘Mass and spin renormalization in Lorentz electrodynamics,’ Annals Phys. (NY) (in press 2000)Google Scholar
  4. 4.
    J.D. Bekenstein, Phys. Rev. D. 7, 2333 (1973)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    G. Bauer, D. Dürr, ‘The Maxwell-Lorentz system of a rigid charge distribution,’ Preprint, Ludwig Maximilian Universität München (1999)Google Scholar
  6. 6.
    W. Braun, K. Hepp, Commun. Math. Phys. 56, 101 (1977)CrossRefADSMathSciNetzbMATHGoogle Scholar
  7. 7.
    P.A.M. Dirac, Proc. Roy. Soc. A 167, 148 (1938)zbMATHCrossRefADSGoogle Scholar
  8. 8.
    J. Ehlers, ‘General relativity and kinetic theory.’ In: General relativity and cosmology, Proceedings of the International School of Physics Enrico Fermi vol. 47, ed. by R. K. Sachs (Academic Press, New York 1971), pp. 1–70Google Scholar
  9. 9.
    H.-P. Gittel, J. Kijowski, E. Zeidler, Commun. Math. Phys. 198, 711 (1998)zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    R. Glassey, J. Schaeffer, Comm. Math. Phys. 119, 353 (1988)zbMATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    R. Glassey, W. Strauss, Comm. Math. Phys. 113 191 (1987)zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    R. Glassey, W. Strauss, Arch. Rat. Mech. Analysis 92, 59 (1986)zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    S. Hawking, Comm. Math. Phys. 43, 199 (1975)CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    D.C. Heggie, Mon. Not. R. astr. Soc. 173, 729 (1975)ADSGoogle Scholar
  15. 15.
    J.D. Jackson, Classical Electrodynamics, 3rd ed., (Wiley, New York 1999)zbMATHGoogle Scholar
  16. 16.
    M. K.-H. Kiessling, Phys. Lett. A 258, 197 (1999)zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    A. Komech H. Spohn, M. Kunze, Commun. PDE 22, 307 (1997)zbMATHMathSciNetGoogle Scholar
  18. 18.
    A. Komech M. Kunze, H. Spohn, Commun. Math. Phys. 203, 1 (1999)zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    A. Komech H. Spohn, ‘Long-time asymptotics for the coupled Maxwell-Lorentz Equations,’ J. Diff. Equations (in press)Google Scholar
  20. 20.
    M. Kunze, H. Spohn, ‘Adiabatic limit of the Maxwell-Lorentz equations,’ Ann. Inst. H. Poincaré, Phys. Theor. (in press)Google Scholar
  21. 21.
    M. Kunze, H. Spohn, ‘Radiation reaction and center manifolds,’ SIAM J. Math. Anal. (in press)Google Scholar
  22. 22.
    J.M. Lévy-Leblond, J. Math. Phys. 10, 806 (1969)CrossRefADSGoogle Scholar
  23. 23.
    E.H. Lieb, Bull. Am. Math. Soc. 22, 1 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    E.H. Lieb, W. Thirring, Ann. Phys. 155, 494 (1984)CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    E.H. Lieb, H.T. Yau, Commun. Math. Phys. 112, 147 (1987)zbMATHCrossRefADSMathSciNetGoogle Scholar
  26. 26.
    H.A. Lorentz, Arch. Néerl. Sci. Exactes Nat. 25, 363 (1892)Google Scholar
  27. 27.
    H.A. Lorentz, Proc. Acad. Wet. Amsterdam, 6 (1904)Google Scholar
  28. 28.
    H.A. Lorentz, The Theory of electrons and its applications to the phenomena of light and radiant heat, (Dover, New York 1952)Google Scholar
  29. 29.
    C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman Co., New York 1973)Google Scholar
  30. 30.
    J.S. Nodvik, Ann. Phys. 28, 225 (1964)CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    D. Noja, A. Posilicano, Delta interactions and electrodynamics of point particles, LANL e-print math-ph/9907009 (1999)Google Scholar
  32. 32.
    W. Pauli, Theory of relativity, Dover (1958)Google Scholar
  33. 33.
    R. Penrose, The emperors new mind, (Oxford Univ. Press, Oxford 1989)Google Scholar
  34. 34.
    G. Rein, The Vlasov-Einstein system with surface symmetry, Habilitationsschrift, Ludwig Maximilian Universität München (1995)Google Scholar
  35. 35.
    F. Rohrlich, Classical charged particles, (Addison Wesley, Redwood City, CA 1990)zbMATHGoogle Scholar
  36. 36.
    A. Sommerfeld, Electrodynamics, (Academic Press, New York 1952)zbMATHGoogle Scholar
  37. 37.
    L.H. Thomas, Nature 117, 514 (1926); Phil. Mag. 3, 1 (1927)ADSCrossRefGoogle Scholar
  38. 38.
    S. Tomonaga, The story of spin, (Univ. Chicago Press, Chicago 1997)Google Scholar
  39. 39.
    G.E. Uhlenbeck, S.A. Goudsmit, Nature 117, 264 (1926)ADSCrossRefGoogle Scholar
  40. 40.
    A.A. Vlasov, Many-particle theory and its application to plasma, (Gordon and Breach, New York, 1961)Google Scholar
  41. 41.
    A.D. Yaghjian, Relativistic dynamics of a charged sphere, Lect. Notes Phys. m11, (Springer, Berlin, 1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michael K.-H. Kiessling
    • 1
  1. 1.Rutgers UniversityPiscatawayUSA

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