International Journal of Theoretical Physics

, Volume 22, Issue 11, pp 981–996 | Cite as

Homotopy construction of a spinor wave functional

  • P. L. Antonelli
  • J. G. Williams


A nonlinear field theory is studied for which the field variables range over a 3-sphere. The Whitehead integral formula is used to construct a double-valued spinor as a functional of the original single-valued field variables.


Field Theory Elementary Particle Quantum Field Theory Field Variable Integral Formula 
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. Aoyama, S. (1977). Nagoya University Physics Department Preprint, DPNU-37-77.Google Scholar
  2. Aoyama, S., and Kodama, Y. (1976).Progress of Theoretical Physics,56, 1970.Google Scholar
  3. Conner, P. E., and Floyd, E. E. (1964).Differentiable Periodic Maps. Springer-Verlag, Berlin.Google Scholar
  4. De Ritis, R., Finkelstein, D., Pisello, D. M., and Weil, D. (1978).Il Nuovo Cimento,48A, 184.Google Scholar
  5. De Vega, H. J. (1978).Physical Review D,18, 2945.Google Scholar
  6. Edwards, S. F. (1968).Journal of Physics A,1, 15.Google Scholar
  7. Enz, U. (1963).Physical Review,131, 1392.Google Scholar
  8. Finkelstein, D. (1955).Physical Review,100, 924.Google Scholar
  9. Finkelstein, D. (1966).Journal of Mathematical Physics,7, 1218.Google Scholar
  10. Finkelstein, D., and Misner, C. W. (1959).Annals of Physics,6, 230.Google Scholar
  11. Finkelstein, D., and Rubinstein, J. (1968).Journal of Mathematical Physics,9, 1762.Google Scholar
  12. Finkelstein, D., and Williams, J. G. (1984).International Journal of Theoretical Physics, to appear.Google Scholar
  13. Flanders, H. (1963).Differential Forms. Academic Press, New York.Google Scholar
  14. Goldhaber, A. S. (1976).Physical Review Letters,36, 1122.Google Scholar
  15. Guillemin, V. W., and Golubitsky, M. (1973).Singularities of Differentiable Mappings. Springer-Verlag, Berlin.Google Scholar
  16. Hellsten, H. (1979).Journal of Mathematical Physics,20, 2431.Google Scholar
  17. Hellsten, H. (1980a). On the Visual Geometry of Spinors and Twistors, appeared inCosmology and Gravitation; Spin, Torsion and Supergravity, NATO Advanced Study Institute Series: Series B, Physics: Volume 58, P. G. Bergmann and Venzo De Sabbata, eds. Plemun Press, New York.Google Scholar
  18. Hellsten, H. (1980b).A Visually Geometric Foundation of Spinor and Twistor Algebra. Fysiska Institutionen, Stockholm, Sweden.Google Scholar
  19. Hilton, P. J. (1966).An Introduction to Homotopy Theory. Cambridge University Press, London.Google Scholar
  20. Hilton, P. J., and Wylie, S. (1967).Homology Theory. Cambridge University Press, London.Google Scholar
  21. Husemoller, D. (1974).Fiber Bundles. Springer-Verlag, Berlin.Google Scholar
  22. Kervaire, M. (1953).Académie des Sciences (Paris), Comptes Rendus,237, 1486.Google Scholar
  23. Kimstedt, C. (1979).Il Nuovo Cimento,53A, 133.Google Scholar
  24. Leinaas, J. M. (1978).Il Nuovo Cimento,47A, 19.Google Scholar
  25. Mandelstam, S. (1975).Physical Review D,11, 3026.Google Scholar
  26. Marx, E. (1969).Il Nuovo Cimento,60A, 683.Google Scholar
  27. Milnor, J. W. (1972).Topology from the Differentiable Viewpoint. University Press of Virginia, Charlottesville, Virginia.Google Scholar
  28. Minami, M. (1979).Progress of Theoretical Physics,62, 1128.Google Scholar
  29. Minami, M. (1980),Progress of Theoretical Physics,63, 303.Google Scholar
  30. Montgomery, D., and Zippin, L. (1955).Topological Transformation Groups. Interscience, New York.Google Scholar
  31. Nicole, D. A. (1978).Journal of Physics G,4, 1363.Google Scholar
  32. Pak, N. K., and Tze, H. C. (1979).Annals of Physics,117, 164.Google Scholar
  33. Patani, A., Schlindwein, M., and Shafi, Q. (1976).Journal of Physics A,9, 1513.Google Scholar
  34. Pisello, D. M. (1977).International Journal of Theoretical Physics,16, 863.Google Scholar
  35. Pisello, D. M. (1978).International Journal of Theoretical Physics,17, 143.Google Scholar
  36. Pisello, D. M. (1979).Gravitation, Electromagnetism and Quantized Charge. Ann Arbor Science Publishers, Ann Arbor, Michigan.Google Scholar
  37. Ragiadakos, Ch. (1980).Canadian Journal of Physics,58, 554.Google Scholar
  38. Ringwood, G. A. (1979).Il Nuovo Cimento,54A, 483.Google Scholar
  39. Ringwood, G. A., and Woodward, L. M. (1981).Physical Review Letters,47, 625.Google Scholar
  40. Ryder, L. H. (1980).Journal of Physics A,13, 437.Google Scholar
  41. Schulman, L. (1968).Physical Review,176, 1558.Google Scholar
  42. Skyrme, T. H. R. (1958).Proceedings of the Royal Society of London,A247, 260.Google Scholar
  43. Skyrme, T. H. R. (1961a).Proceedings of the Royal Society of London,A260, 127.Google Scholar
  44. Skyrme, T. H. R. (1961b).Proceedings of the Royal Society of London,A262, 237.Google Scholar
  45. Skyrme, T. H. R. (1962).Nuclear Physics,31, 556.Google Scholar
  46. Skyrme, T. H. R. (1971).Journal of Mathematical Physics,12, 1735.Google Scholar
  47. Spanier, E. H. (1966).Algebraic Topology. McGraw-Hill, New York.Google Scholar
  48. Steenrod, N. (1951).Topology of Fiber Bundles. Princeton University Press, Princeton, New Jersey.Google Scholar
  49. Stong, R. E. (1968).Notes on Cobordism Theory. Princeton University Press, Princeton, New Jersey.Google Scholar
  50. Whitehead, J. H. C. (1947).Proceedings of the National Academy of Sciences USA,33, 117.Google Scholar
  51. Williams, J. G. (1970).Journal of Mathematical Physics,11, 2611.Google Scholar
  52. Williams, J. G. (1979).Canadian Journal of Physics,57, 590.Google Scholar
  53. Williams, J. G., and Zvengrowski, P. (1977).International Journal of Theoretical Physics,16, 755.Google Scholar
  54. Woo, G. (1977).Journal of Mathematical Physics,18, 1756.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • P. L. Antonelli
    • 1
  • J. G. Williams
    • 2
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsOkanagan CollegeVernonCanada

Personalised recommendations