General Relativity and Gravitation

, Volume 14, Issue 7, pp 615–620 | Cite as

Half-integral spin from quantum gravity

  • John L. Friedman
  • Rafael D. Sorkin
Research Articles


For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values. In the absence of a full theory of quantum gravity, this result relies on a set of apparently natural assumptions governing the kinematics of such a theory. A key feature is that state vectors are in general invariant only under asymptotically trivial diffeomorphisms that can be continuously deformed to the identity. Angular momentum is associated with diffeomorphisms that look asymptotically like rotations; and the question of whether half-integral values occur depends on whether the diffeomorphism associated with a 2π rotation is itself deformable to the identity.


Angular Momentum State Vector Quantum Gravity 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Trautman, A. (1965). InLectures on General Relativity (Prentice Hall, Englewood Cliffs, New Jersey).Google Scholar
  2. 2.
    Wess, J., and Zumino, B. (1974).Nucl. Phys. B,70, 39.Google Scholar
  3. 3.
    Wheeler, J. A. (1968). InBattelles Recontres: 1967 Lectures in Mathematics and Physics, eds. C. DeWitt and J. A. Wheeler (W. A. Benjamin, New York).Google Scholar
  4. 4.
    Finkelstein, D., and Misner, C. (1959).Ann. Phys. (N. Y.).,6, 230.Google Scholar
  5. 5.
    Williams, J. G. (1971).J. Math. Phys.,12, 308; Williams, J. G., and Zvengrowski, P. (1977).Int. J. Theor. Phys.,16, 756.Google Scholar
  6. 6.
    Jackiw, R., and Rebbi, C. (1976).Phys. Rev. Lett.,36, 1116; Hasenfratz, P., and 't Hooft, G. (1976).Phys. Rev. Lett.,36, 1119.Google Scholar
  7. 7.
    Friedman, J. L., and Sorkin, R. D. (1980).Phys. Rev. Lett.,44, 1100.Google Scholar
  8. 8.
    Higgs, P. W. (1958).Phys. Rev. Lett.,1, 373.Google Scholar
  9. 9.
    Jackiw, R. (1980).Rev. Mod. Phys.,52, 661.Google Scholar
  10. 10.
    Hendricks, H. (1977).Bull. Soc. Math. France, Memoire,53, 81; see §4.3.Google Scholar
  11. 11.
    Barut, A. O. (1974).Phys. Rev. D,10, 2712; Goldhaber, A. S., (1976).Phys. Rev. Lett.,36, 1122; Tolkachev, E. A., and Tomil'chik, L. M. (1979).Phys. Lett.,818, 173; Friedman, J. L., and Sorkin, R. D. (1980).Commun. Math. Phys.,73, 161.Google Scholar
  12. 12.
    Friedman, J. L., and Sorkin, R. D. to be published.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • John L. Friedman
    • 1
  • Rafael D. Sorkin
    • 2
  1. 1.Physics DepartmentUniversity of WisconsinMilwaukee
  2. 2.Institute for Advanced StudyPrinceton

Personalised recommendations