Advertisement

General Relativity and Gravitation

, Volume 13, Issue 2, pp 175–187 | Cite as

On pseudoparticle solutions in Yang's theory of gravity

  • Eckehard W. Mielke
Research Articles

Abstract

Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to “pure” gravitational fields. In afour-dimensional Riemannian manifold it is shown that thedouble self-dual solutions obey Einstein's vacuum equations with the cosmological term, whereas the doubleanti-self-dual configurations satisfy the Rainich conditions of Wheeler'sgeometrodynamics. Conformal methods reveal that the gravitational analog of the “instanton” or pseudoparticle solution of Yang-Mills theory was already known to Riemann.

Keywords

Manifold Gauge Theory Riemannian Manifold Differential Geometry Gravitational Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atiyah, M. F., Hithcin, N. J., and Singer, I. M. (1978).Proc. R. Soc. London Ser. A,362, 425.Google Scholar
  2. 2.
    de Alfaro, V., Fubini, S., and Furlan, G. (1978).Phys. Lett.,73B, 463.Google Scholar
  3. 3.
    de Alfaro, V., Fubini, S., and Furlan, G. (1979).Nuovo Cimento,50A, 523.Google Scholar
  4. 4.
    Bach, R. (1921).Math. Z.,9, 110.Google Scholar
  5. 5.
    Belavin, A. A., Polyakov, A. M., Schwartz, A. S., and Tyupkin, Yu. S. (1975).Phys. Lett.,59B, 85 (1975).Google Scholar
  6. 6.
    Belavin, A. A., and Burlankov, D. E. (1976).Phys. Lett.,58A, 7.Google Scholar
  7. 7.
    Belinskii, V. A., Gibbons, G. W., Page, D. N., and Pope, C. N. (1978).Phys. Lett.,76B, 433.Google Scholar
  8. 8.
    Brill, D. R., and Wheeler, J. A. (1957).Rev. Mod. Phys.,29, 465; (1961).Ibid., (E)33, 623.Google Scholar
  9. 9.
    Charap, J. M., and Duff, M. J. (1977).Phys. Lett.,69B, 445; (1977).Ibid.,71B, 219.Google Scholar
  10. 10.
    Chern, S. S. (1945).Ann. Math.,46, 674.Google Scholar
  11. 11.
    Debney, G., Fairchild, E. E., Jr., and Siklos, S. T. C. (1978).Gen. Rel. Grav.,9, 879.Google Scholar
  12. 12.
    Deser, S. (1975). InQuantum Gravity, eds. Isham, C. J., Penrose, R., and Sciama, D. W., Clarendon Press, Oxford, p. 136.Google Scholar
  13. 13.
    Eguchi, T., and Freund, P. G. O. (1976).Phys. Rev. Lett.,37, 1251.Google Scholar
  14. 14.
    Eguchi, T., and Hanson, A. J. (1978).Phys. Lett.,74B, 249; (1979).Ann. Phys. (N.Y.),120, 82.Google Scholar
  15. 15.
    Fairchild, E. E., Jr., (1976).Phys. Rev. D,14, 384; (1977).Ibid.,16, 2438.Google Scholar
  16. 16.
    Geroch, R. (1966).Ann. Phys. (N.Y.),36, 147.Google Scholar
  17. 17.
    Gibbons, G. W., and Hawking, S. W. (1978).Phys. Lett.,78B, 430.Google Scholar
  18. 18.
    Gibbons, G. W., and Hawking, S. W. (1979).Commun. Math. Phys.,66, 291.Google Scholar
  19. 19.
    Gibbons, G. W., and Pope, C. N. (1979).Commun. Math. Phys.,66, 267.Google Scholar
  20. 20.
    Gu, C.-H., Hu, H.-S., Li, O.-Q., Shen, C.-L., Xin, Y.-L., and Yang, C.-H. (1978).Sci. Sin.,11, 475.Google Scholar
  21. 21.
    Hawking, S. W. (1977).Phys. Lett.,60A, 81.Google Scholar
  22. 22.
    Hawking, S. W.Euclidean Quantum Gravity, to appear in 1978 Cargese Lectures on Gravitation, eds. Deser, S., and Levy, M., Plenum, New York.Google Scholar
  23. 23.
    Hawking, S. W., and Pope, C. N. (1978).Nucl. Phys. B,146, 381.Google Scholar
  24. 24.
    Hehl, F. W., Ne'eman, Y., Nitsch, J., and Von der Heyde, P. (1978).Phys. Lett.,78B, 102.Google Scholar
  25. 25.
    Jackiw, R. (1977).Rev. Mod. Phys.,49, 681.Google Scholar
  26. 26.
    Kazdan, J. L., and Warner, F. W. (1975).J. Diff. Geom.,10, 113.Google Scholar
  27. 27.
    Kobayashi, S., and Nomizu, K. (1963, 1969).Foundations of Differential Geometry, Vols. I and II, Interscience, New York.Google Scholar
  28. 28.
    Lanczos, C. (1938).Ann. Math.,39, 842.Google Scholar
  29. 29.
    Lanczos, C. (1949).Rev. Mod. Phys.,21, 497.Google Scholar
  30. 30.
    Mielke, E. W. (1977).Gen. Rel. Grav.,8, 175.Google Scholar
  31. 31.
    Mielke, E. W. (1977).Gen. Rel. Grav.,8, 321.Google Scholar
  32. 32.
    Mielke, E. W. (1978).Phys. Rev. D,18, 4525.Google Scholar
  33. 33.
    Misner, C. W. (1963).Ann. Phys. (N. Y.),24, 102.Google Scholar
  34. 34.
    Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation, Freeman, San Francisco, quoted as MTW.Google Scholar
  35. 35.
    Misner, C. W., and Wheeler, J. A. (1957).Ann. Phys. (N. Y.),2, 525, reprinted in Wheeler, J. A. (1962).Geometrodynamics, Academic, New York.Google Scholar
  36. 36.
    Olesen, P. (1977).Phys. Lett.,71B, 189.Google Scholar
  37. 37.
    Page, D. N. (1978).Phys. Lett.,78B, 249.Google Scholar
  38. 38.
    Pope, C. N., and Yuille, A. L. (1978).Phys. Lett.,78B, 424.Google Scholar
  39. 39.
    Rainich, G. Y. (1925).Trans. Am. Math. Soc.,27, 106.Google Scholar
  40. 40.
    Rosen, G. (1959).Phys. Rev.,114, 1179.Google Scholar
  41. 41.
    Rund, H., and Lovelock, D. (1972).Jahresber. Deutsch. Math.-Verein,74, 1.Google Scholar
  42. 42.
    Salam, Abdus, and Strathdee, J. (1978).Phys. Rev. D,18, 4480.Google Scholar
  43. 43.
    Sezgin, E., and van Nieuwenhuizen, P. (1979). “New ghost-free gravity Lagangians with propagating torsion,” preprint.Google Scholar
  44. 44.
    Stelle, K. S. (1977).Phys. Rev. D,16, 953.Google Scholar
  45. 45.
    Stephenson, G. (1958).Nuovo Cimento,IX, 263.Google Scholar
  46. 46.
    Trautman, A. (1979).Czech. J. Phys.,B29, 107.Google Scholar
  47. 47.
    Weyl, H. (1919).Ann. Phys. (Leipzig),59, 101.Google Scholar
  48. 48.
    White, J. H. (1975). inProc. Symp. Pure Math.,XXVII(l), American Mathematical Society, Providence, Rhode Island, p. 429.Google Scholar
  49. 49.
    Wilczek, F. inQuark Confinement and Field Theory, eds. Stump, D., and Weingarten, D. Wiley, New York, p. 211.Google Scholar
  50. 50.
    Witten, E. (1977).Phys. Rev. Lett.,38, 121.Google Scholar
  51. 51.
    Wolf, J. A. (1974).Spaces of Constant Curvature, Publish or Perish, Boston.Google Scholar
  52. 52.
    Xin, Y. L. (1980).J. Math. Phys.,21, 343.Google Scholar
  53. 53.
    Yamabe, H. (1960).Osaka Math. J.,12, 12.Google Scholar
  54. 54.
    Yang, C. N. (1974).Phys. Rev. Lett.,33, 445.Google Scholar
  55. 55.
    Yang, C. N., and Mills, R. L. (1954).Phys. Rev.,96, 191.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Eckehard W. Mielke
    • 1
  1. 1.International Centre for Theoretical PhysicsTriesteItaly

Personalised recommendations