Skip to main content
SpringerLink
Log in

Lagrangian dynamics of spinning particles and polarized media in general relativity

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Israel, W.: Lettere al Nuovo Cimento7, 860 (1973)

    Google Scholar 

  2. Suttorp, L. G., de Groot, S. R.: Foundations of electrodynamics, Chapters 4, 5, § 7, Amsterdam: North-Holland 1972

    Google Scholar 

  3. Halbwachs, F.: Théorie relativiste des fluides a spin. Paris: Gauthier-Villars 1960

    Google Scholar 

  4. Corben, H.C.: Classical and quantum theories of spinning particles. New York: Holden-Day 1967

    Google Scholar 

  5. Mathisson, M.: Z. Physik67, 826 (1931);

    Google Scholar 

  6. : Proc. Cambridge Phil. Soc.38, 40 (1942)

    Google Scholar 

  7. Papapetrou, A.: Praktika de l'Akademie d'Athenes14, 540 (1939);

    Google Scholar 

  8. : Proc. Roy. Soc. London A209, 248 (1951)

    Google Scholar 

  9. Taub, A.H.: J. Math. Phys.5, 112 (1964);

    Google Scholar 

  10. Proceedings of the Galileo Galilei centenary meeting on general relativity, p. 1. Firenze: G. Barbera 1965

  11. Dixon, W.G.: Nuovo Cimento34, 317 (1964);

    Google Scholar 

  12. : J. Math. Phys.8, 1591 (1967);

    Google Scholar 

  13. : Proc. Roy. Soc. London A314, 499 (1970); A319, 509 (1970)

    Google Scholar 

  14. Madore, J.: Ann. Inst. Henri Poincaré11, 221 (1969);

    Google Scholar 

  15. : C. R. Acad. Sci. Paris273A, 782 (1971)

    Google Scholar 

  16. Das, A.: Progr. Theoret. Phys.23, 610 (1960); Tulczyjew, W.: Acta Phys. Polon.18, 393 (1959); Westfahl, K.: Ann. Physik20, 241 (1967)

    Google Scholar 

  17. Pryce, M.H.L.: Proc. Roy. Soc. London A195, 62 (1948); Møller, C.: Ann. Inst. Henri Poincaré11, 251 (1949); Beiglböck, W.D.: Commun. math. Phys.5, 106 (1967)

    Google Scholar 

  18. Frenkel, J.: Z. Physik37, 243 (1926)

    Google Scholar 

  19. Barut, A.O.: Electrodynamics and classical theory of fields and particles, p. 77. New York: MacMillan 1964

    Google Scholar 

  20. Künzle, H.P.: J. Math. Phys.13, 739 (1972);

    Google Scholar 

  21. : Commun. math. Phys.27, 23 (1972)

    Google Scholar 

  22. Duval, C., Fliche, H.H., Souriau, J.M.: C. R. Acad. Sci. Paris274, 1082 (1972)

    Google Scholar 

  23. Bargmann, V., Michel, L., Telegdi, V.L.: Phys. Rev. Letters2, 435 (1959); Weyssenhoff, J., Raabe, A.: Acta Phys. Polon.9, 46 (1947)

    Google Scholar 

  24. Pauli, W.: Theory of relativity (transl. by G. Field, § 35 and p. 216. New York: Pergamon 1958

    Google Scholar 

  25. Møller, C.: Theory of relativity, Chapter 7. Oxford: Clarendon Press 1972

    Google Scholar 

  26. Penfield, P., Haus, H.A.: Electrodynamics of moving media. Cambridge, Mass.: M. I. T. Press 1967

    Google Scholar 

  27. Minkowski, H.: (a) Nachr. Ges. Wiss. Göttingen53 (1908),

  28. : Math. Ann.68, 472 (1910); Abraham, M.: Ann. Physik44, 537 (1914); Einstein, A., Laub, J.: Ann. Physik26, 541 (1908)

    Google Scholar 

  29. de Groot, S.R., Suttorp, L.G.: Physica39, 84 (1968)

    Google Scholar 

  30. Grot, R.A., Eringen, A.C.: Int. J. Engng. Sci.4, 610 (1966)

    Google Scholar 

  31. Rosenfeld, L.: Mem. Acad. Roy. Belg.18, fasc. 6 (1940); Belinfante, F.J.: Physica6, 887 (1939)

  32. Taub, A.H.: In: Cattaneo, C. (Ed.): Relativistic fluid dynamics, p. 266; Bressanone: C.I.M.E. 1971; Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time, p. 69. New York: Cambridge U.P. 1973

    Google Scholar 

  33. Maugin, G.A.: Ann. Inst. Henri Poincaré15, 275 (1971)

    Google Scholar 

  34. Weyl, H.: Phys. Rev.77, 699 (1950)

    Google Scholar 

  35. Sciama, D.W.: J. Math. Phys.2, 472 (1961)

    Google Scholar 

  36. Kibble, T.W.B.: J. Math. Phys.2, 212 (1961)

    Google Scholar 

  37. Hehl, F.W.: GRG Journ.4, 333 (1973);5, 491 (1974)

    Google Scholar 

  38. Trautman, A.: Bull. Acad. Polon. Sci.20, 185, 503 (1972);

    Google Scholar 

  39. : Symposia Mathematica12, 139 (1973)

    Google Scholar 

  40. Isham, C.J., Salam, A., Strathdee, J.: Nature (Phys. Sci.)244, 82 (1973)

    Google Scholar 

  41. Trautman, A.: Nature (Phys. Sci.)242, 7 (1973); Stewart, J., Hâjiček, P.: Nature (Phys. Sci.)244, 96 (1973); Copzýnski, W.: Phys. Lett. A43, 63 (1973)

    Google Scholar 

  42. Lovelock, D.: J. Math. Phys.13, 874 (1972)

    Google Scholar 

  43. Weyl, H.: Space, time, matter, p. 230. New York: Dover 1951

  44. De Wet, J.S.: Proc. Cambridge Phil. Soc.44, 546 (1948); Chang, T.S.: Proc. Cambridge Phil. Soc.44, 70 (1948)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Alberta, Edmonton, Canada

    Ian Bailey

  2. Theoretical Physics Institute, Physics Department, University of Alberta, Edmonton, Canada

    Werner Israel

Authors
  1. Ian Bailey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Werner Israel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. Ehlers

Work partially supported by the National Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bailey, I., Israel, W. Lagrangian dynamics of spinning particles and polarized media in general relativity. Commun.Math. Phys. 42, 65–82 (1975). https://doi.org/10.1007/BF01609434

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01609434

Keywords

Search

Navigation