Generalised quaternion methods in conformal geometry

  • Eric A. Lord


A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.


Field Theory Elementary Particle Quantum Field Theory Equivalent Statement Covariant Formulation 
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. Barut, A. O. (1968).Physical Review Letters,20, 893.Google Scholar
  2. Cayley, A. (1879).Mathematische Annalen,15.Google Scholar
  3. Coxeter, H. S. M. (1936).Annals of Mathematics,37, 418.Google Scholar
  4. Coxeter, H. S. M. (1943).American Mathematical Monthly,50, 217.Google Scholar
  5. Dirac, P. A. M. (1936).Annals of Mathematics,37, 429.Google Scholar
  6. Fierz, M. (1936).Zeitschrift für Physik,102, 527.Google Scholar
  7. Hamilton, W. R. (1844).Philosophical Magazine,2, 489.Google Scholar
  8. Hamilton, W. R. (1866).Elements of Quaternions. Longmans.Google Scholar
  9. Hodge, W. V. D. and Pedoe, D. (1968).Methods of Algebraic Geometry, Vol. 2, Cambridge University Press.Google Scholar
  10. ten Kate, A. (1968).Journal of Mathematical Physics,9, 181.Google Scholar
  11. Kilmister, C. W. (1953).Proceedings of the Royal Irish Academy,A55, 73.Google Scholar
  12. Kilmister, C. W. (1955).Proceedings of the Royal Irish Academy,A57, 37.Google Scholar
  13. Klein, F. (1884).Vorlesungen über das Ikosaeder. Leipzig. (English Translation, Dover, 1956.)Google Scholar
  14. Klein, F. (1911).Physikalische Zeitscherift,12, 17.Google Scholar
  15. Klein, F. (1926).Vorlesungen über Höhere Geometrie. Berlin.Google Scholar
  16. Kofink, W. (1937).Annalen der Physik,30, 91.Google Scholar
  17. Kofink, W. (1940).Annalen der Physik,37, 421.Google Scholar
  18. Lord, E. A. (1972a).International Journal of Theoretical Physics, Vol. 5, No. 5, p. 339.Google Scholar
  19. Lord, E. A. (1972b).Journal of Mathematical Sciences and Applications 40, 509.Google Scholar
  20. Lord, E. A. (1974).International Journal of Theoretical Physics, Vol. 9, No. 2, p. 117.Google Scholar
  21. Mack, G. and Salam, A. (1969).Annals of Physics,53, 174.Google Scholar
  22. Pauli, W. (1927).Zeitschrift für Physik,63, 601.Google Scholar
  23. Pauli, W. (1936).Annales de l'Institut Henri Poincaré,6, 109.Google Scholar
  24. Penrose, R. (1964).Relativity, Groups and Topology (Eds. de Witt and de Witt). Blackie.Google Scholar
  25. Penrose, R. (1967).Journal of Mathematical Physics,8, 345.Google Scholar
  26. Penrose, R. (1969).International Journal of Theoretical Physics, Vol. 2, No. 1, p. 38.Google Scholar
  27. Rastall, P. (1964).Reviews of Modern Physics,36, 820.Google Scholar
  28. Sachs, R. K. (1964).Relativity, Groups and Topology (Eds. de Witt and de Witt). Blackie.Google Scholar
  29. Salam, A. and Strathdee, J. (1969).Physical Review,184, 1760.Google Scholar
  30. Silberstein, L. (1912).Philosophical Magazine,23, 790.Google Scholar
  31. Silberstein, L. (1913).Philosophical Magazine,25, 135.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • Eric A. Lord
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations