On Kähler’s Geometric Description of Dirac Fields

  • M. Göckeler
  • H. Joos
Part of the NATO ASI Series book series (NSSB, volume 115)


The lattice approximation of gauge fields is based on their geometric interpretation. In a similar way, a differential geometric generalization of the Dirac equation due to E. Kähler1 seems to be an appropriate starting point for the lattice approximation of matter fields2,3. It is the purpose of this lecture to illustrate several aspects of this approach.


Gauge Transformation Dirac Equation Differential Form Gauge Field Lattice Approximation 
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.
    E. Kähler, Rend. Math. Ser. V, 21, 425 (1962).Google Scholar
  2. 2.
    P. Becher and H. Joos, Z. Physik C-Particles and Fields 15, 343 (1982).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    J.M. Rabin, Nucl. Phys. B201, 315 (1982).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    W. Graf, Ann. Inst. H. Poincare, Sect. A 29, 85 (1978).MathSciNetMATHGoogle Scholar
  5. 5.
    T. Banks, Y. Dothan, and D. Horn, Phys. Lett. 117B, 413 (1982).MathSciNetADSGoogle Scholar
  6. 6.
    I.M. Benn and R.W. Tucker, Comm. Math. Phys. 89, 341 (1983).MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    I.M. Singer and J.A. Thorpe, “Lecture Notes on Elementary Topology and Geometry”, Scott, Foresman, Glenview, III. (1967).Google Scholar
  8. 8.
    L. Susskind, Phys. Rev. D16, 3031 (1977).ADSGoogle Scholar
  9. 9.
    H.S. Sharatchandra, H.J. Thun, and P. Weisz, Nucl. Phys. B192, 205 (1981).ADSCrossRefGoogle Scholar
  10. 10.
    N. Kawamoto and J. Smit, Nucl. Phys. B192, 100 (1981).ADSCrossRefGoogle Scholar
  11. 11.
    M. Göckeler, Z. Physik C-Particles and Fields 18, 323 (1983).ADSCrossRefGoogle Scholar
  12. 12.
    A. Chodos and J.B. Healy, Nucl. Phys. B127, 426 (1977).ADSCrossRefGoogle Scholar
  13. 13.
    W. Celmaster and F. Krausz, Nucl. Phys. B220 FS8, 434 (1983)ADSCrossRefGoogle Scholar
  14. W. Celmaster and F. Krausz, Phys. Rev. D28, 1527 (1983).ADSGoogle Scholar
  15. 14.
    J. Kogut, M. Stone, H.W. Wyld, S.H. Shenker, J. Shigemitsu, and D.K. Sinclair, Nucl. Phys. B225 FS9, 326 (1983).ADSCrossRefGoogle Scholar
  16. 15.
    B.K. Vainshtein, “Modern Crystallography I”, Springer-Verlag, Berlin, Heidelberg, New York (1981).Google Scholar
  17. 16.
    B. Berg and A. Billoire, Nucl. Phys. B221, 109 (1983).ADSCrossRefGoogle Scholar
  18. 17.
    G. Parisi and Zhang Yi-Cheng, I.N.F.N.-Sezione di Roma preprint n. 357 (1983).Google Scholar
  19. 18.
    I.M. Benn and R.W. Tucker, Phys. Lett. 125B, 47 (1983).ADSGoogle Scholar
  20. 19.
    S. Elitzur, E. Rabinovici, and A. Schwimmer, Phys. Lett. 119B, 165 (1982); H. Aratyn and A.H. Zimerman, preprint DESY 83-075 (1983).MathSciNetADSGoogle Scholar
  21. 20.
    P. Becher, in: “Proceedings of the 7th Johns Hopkins Workshop on Current Problems in High Energy Particle Theory” (Bad Honnef, 1983), to appear.Google Scholar
  22. 21.
    H.K. Nickerson, D.C. Spencer, and N.E. Steenrod, “Advanced calculus”, van Nostrand Comp., Princeton, N.J. (1959).Google Scholar
  23. 22.
    I.M. Benn and R.W. Tucker, Phys. Lett. 119B, 348 (1982).ADSGoogle Scholar
  24. 23.
    T. Banks, S. Raby, L. Susskind, J. Kogut, D.R.T. Jones, P.N. Scharbach, and D. Sinclair, Phys. Rev. D15, 1111 (1976).ADSGoogle Scholar
  25. 24.
    P. Becher and H. Joos, Lett. Nuovo Cim. 38, 293 (1983).CrossRefGoogle Scholar
  26. 25.
    A.N. Burkitt, A. Kenway, and R.D. Kenway, Phys. Lett. 128B, 83 (1983)ADSGoogle Scholar
  27. P. Mitra, Phys. Lett. 123B, 77 (1983).ADSGoogle Scholar
  28. 26.
    P. Mitra, Nucl. Phys. B227, 349 (1983).ADSCrossRefGoogle Scholar
  29. 27.
    P. Mitra and P. Weisz, Phys. Lett. 126B, 355 (1983).ADSGoogle Scholar
  30. 28.
    O. Napoly, Cen-Saclay preprint SPh. T/83/77 (1983).Google Scholar
  31. 29.
    M. Göckeler, Nucl. Phys. B224, 508 (1983).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • M. Göckeler
    • 1
  • H. Joos
    • 1
  1. 1.Deutsches Elektronen-Synchrotron DESYHamburgGermany

Personalised recommendations