Skip to main content
SpringerLink
Log in

Relativistic Boltzmann Theory

  • Conference paper
The Boltzmann Equation

Part of the book series: Acta Physica Austriaca ((FEWBODY,volume 10/1973))

  • 657 Accesses

Summary

In the last thirty years a relativistic kinetic theory of transport processes has been developed, which is based on an appropriate generalization of Boltzmann’s celebrated equation. The relevant macroscopic laws could be derived in the framework of this theory. Moreover transport coefficients could be calculated, according to various procedures:

  1. (a)

    the eigenvalue method,

  2. (b)

    the simplified collision description,

  3. (c)

    the moment method and

  4. (d)

    the orthogonal functions method.

The last — new — method is free from the limitations, inherent in the first three. In fact it allows to find values for the relativistic transport coefficients of systems of particles with arbitrary cross-sections in successive approximations Results are presented for the heat conductivity, the viscosities and the coefficient of sound absorption of simple relativistic gases with different cross-sections, in various approximations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Lichnerowicz and R. Marrot, Compt. Rend. Acad. Sc., Paris 210 (1940) 759; 211 (1940) 177; 219 (1944) 270.

    Google Scholar 

  2. R. Marrot, Journ. Math. pures et appliquées 25 (1946) 12.

    MathSciNet  Google Scholar 

  3. N.A. Chernikov, Sov. Phys. Doklady 2 (1957) 103, 248; 5 (1960) 764; Naukn. Dokl. Vyssh. Shkoly, Ser. Fiz.-Mat. 1 (1959) 168.

    Google Scholar 

  4. G.E. Tauber and J.W. Weinberg, Phys. Rev. 122 (1961) 1342.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. W. Israel, J. Math. Phys. 4 (1963) 1163.

    Article  ADS  MathSciNet  Google Scholar 

  6. R. Hakim, J. Math. Phys. 8 (1967) 1315, Phys. Rev. 162 (1967) 128.

    Google Scholar 

  7. N.G. van Kampen, Physica 43 (1969) 244.

    Article  ADS  Google Scholar 

  8. Ch.G. van Weert, Proc. Kon. Ned. Akad. Wet., Amsterdam B 73 (1970) 381, 397, 500, 517 (thesis Amsterdam).

    Google Scholar 

  9. S.R. de Groot and L.G. Suttorp, Foundations of electrodynamics (North-Holland) Amsterdam, 1972 (chapter V, section 2a).

    Google Scholar 

  10. W.A. van Leeuwen, Proc. Kon. Ned. Akad. Wet., Amsterdam B 74 (1971) 122, 134, 150, 269, 276 (thesis Amsterdam).

    Google Scholar 

  11. S.R. de Groot, Ch.G. van Weert, W.Th. Hermens and W.A. van Leeuwen, Physica 40 (1968–1969) 257, 581; 42 (1969) 309; Phys. Lett. 26A (1968) 345, 439.

    Google Scholar 

  12. E.C.G. Stueckelberg, Helv. Phys. Acta 25 (1952) 577.

    MATH  MathSciNet  Google Scholar 

  13. W. Iieitler, Ann. Inst. Henri Poincaré 15 (1967) 67.

    Google Scholar 

  14. F. Jüttner, Ann. Physik 34 (1911) 856.

    Article  MATH  Google Scholar 

  15. C. Eckart, Phys. Rev. 58 (1940) 919.

    Article  MATH  ADS  Google Scholar 

  16. G.A. Kluitenberg, S.R. de Groot and P. Mazur, Physica 19 (1953) 689, 1079; 20 (1954) 199; 21 (1955) 148.

    Google Scholar 

  17. W.Th. Iiermens, Proc. Kon. Ned. Akad. Wet., Amsterdam B 74 (1971) 376, 387, 461, 478 (thesis Amsterdam).

    Google Scholar 

  18. W. Th. Hermens, W.A. van Leeuwen, Ch.G. van Weert and S.R. de Groot, Physica 60 (1972) 472

    Article  ADS  Google Scholar 

  19. P. Curie, Oeuvres, p. 118, Paris, 1908.

    Google Scholar 

  20. S.R. de Groot and P. Mazur, Non-equilibrium thermodynamics (North-Holland) Amsterdam, 1962.

    Google Scholar 

  21. L. Onsager, Phys. Rev. 37 (1931) 405; 38 (1931) 2265.

    Article  ADS  Google Scholar 

  22. H.B.G. Casimir, Rev. Mod. Phys. 17 (1945) 343.

    Article  ADS  Google Scholar 

  23. J. Bernstein, G. Feinberg and T.D. Lee, Phys. Rev. 139B (1965) 1650.

    Google Scholar 

  24. C.S. Wang (Chang) and G.E. Uhlenbeck, Rep. M 999, Eng. Res. Inst., Univ. of Michigan, 1952.

    Google Scholar 

  25. L. Waldmann, Z. Naturf. 11A (1956) 523; Encycl. Phys. 12 (1958) 370.

    Google Scholar 

  26. W.A. van Leeuwen and S.R. de Groot, Physica 51 (1971) 1, 16, 32.

    Article  ADS  Google Scholar 

  27. E. Gross, D. Bhatnager and M. Krook, Phys. Rev. 94, (1954) 511.

    Article  MATH  ADS  Google Scholar 

  28. C. Marle, Ann. Inst. Henri Poincaré 10 (1969) 67, 127.

    MathSciNet  Google Scholar 

  29. H. Grad, Comm. Pure Appl. Math. 2 (1949) 331; Phys. Fluids 6 (1963) 147

    Article  MathSciNet  Google Scholar 

  30. W. Israel and J.N. Vardalas, Lett. N. Cim. 4 (1970) 887.

    Article  Google Scholar 

  31. B. Vignon, Ann. Inst. Henri Poincaré 10 (1969) 31.

    MathSciNet  Google Scholar 

  32. J.L. Anderson, Proc. 1969 Relativity conference in the Mid-West (Plenum) New York, 1970.

    Google Scholar 

  33. J.M. Stewart, Non-equilibrium relativistic kinetic theory ( Springer ), Berlin-Heidelberg-New York, 1971.

    Google Scholar 

  34. C.W. Misner, Astrophys. J. 151 (1968) 431.

    Article  ADS  Google Scholar 

  35. S. Chapman, Phil. Trans. Roy. Soc. A 216 (1916) 279; A 217 (1917) 115.

    ADS  Google Scholar 

  36. D. Enskog, Dissertation, Uppsala, 1917.

    Google Scholar 

  37. W.A. van Leeuwen, P.H. Polak and S.R. de Groot, Phys. Lett. 37A (1971) 323; C.R. Acad. Sc., Paris 274 (1972) 431; Physica, to be published.

    Google Scholar 

  38. D.C. Kelly, Unpublished report, Miami University, Oxford, Ohio, 1963. A different set of orthogonal functions was proposed here, but since it is incomplete, no method could be developed from it.

    Google Scholar 

  39. S. Chapman and T.G. Cowling, The mathematical theory of non-uniform gases, Cambridge University Press, 1939 (third edition, 1970 ).

    Google Scholar 

  40. J. Guichelaar, W.A. van Leeuwen and S.R. de Groot, Physica 59 (1972) 97.

    Article  ADS  Google Scholar 

  41. S. Weinberg, Astrophys. J. 168 (1971) 175.

    Article  ADS  Google Scholar 

  42. T.D. Lee, Astrophys. J. 111 (1950) 625.

    Article  ADS  Google Scholar 

  43. M. Ruderman, Rep. Progr. Phys., 28 (1965) 411.

    Article  ADS  Google Scholar 

  44. M. Ruderman,, Acc. Naz. Lincei 368 (1971) 1.

    Google Scholar 

  45. T. de Graaf, Acc. Naz. Lincei 368 (1971) 81.

    Google Scholar 

  46. J. Ehlers, Rendiconti Scuola Int. di Fisica “Enrico Fermi” 47 (1971) 1.

    ADS  MathSciNet  Google Scholar 

  47. W. Israel, in General Relativity, Papers in honour of J.L. Synge (Clarendon Press) Oxford, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands

    S. R. de Groot

Authors
  1. S. R. de Groot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Rockefeller University, New York, N.Y., USA

    E. G. D. Cohen

  2. Institute for Theoretical Physics, University of Vienna, Vienna, Austria

    W. Thirring

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

de Groot, S.R. (1973). Relativistic Boltzmann Theory. In: Cohen, E.G.D., Thirring, W. (eds) The Boltzmann Equation. Acta Physica Austriaca, vol 10/1973. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8336-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-8336-6_21

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-8338-0

  • Online ISBN: 978-3-7091-8336-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation