The Supersymmetry of the Dirac-Yand-Mills Operator and Some Applications

  • L. O’Raifeartaigh


Although sersymmetry first became known within the context of string-theory(1) and field theory(2), and has thus come to be associated with Fermi-Bose symmetry, it is actually a much broader concept(3). In this paper the broader concept of supersymmetry is defined, and it is pointed out that in this broader sense, there exists in nature a fundamental operator, namely the square \( \not D^2 \) of the Dirac, or Yang-Mills operator , where Aμ is the gauge-potential, which is supersymmetric.


Zero Mode Negative Mode Index Theorem Ground State Solution Supersymmetric Quantum Mechanics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Ramond, Phys. Rev. D3, (1971) 2415Google Scholar
  2. J. Scherk, Rev. Mod. Phys. 47 (1975) 1CrossRefGoogle Scholar
  3. F. Gliozzi, D, Olive, J. Scherk, Nucl. Phys. B122 (1977) 253.Google Scholar
  4. 2.
    J. Wess, B. Zumino, Phys. Lett. 49B 1974 52Google Scholar
  5. J. Wess, B. Zumino, Nucl. Phys. B78 (1974) 1CrossRefGoogle Scholar
  6. P. Fayet, S. Ferrara, Phys. Reports 32 (1977) 249CrossRefGoogle Scholar
  7. J. Bagger, J. Wess, Supersymmetry and Supergravity (Princeton Univ. Press 1983).Google Scholar
  8. 3.
    E. Witten, Nucl. Phys. B185 (1981) 513CrossRefGoogle Scholar
  9. E. Witten, J. Diff. Geom. 17 (1982) 661Google Scholar
  10. D. Lancaster, Nuovo Cim. 79A (1984) 28.CrossRefGoogle Scholar
  11. 4.
    G. ‘t Hooft, Nucl. Phys. B79 (1974) 276Google Scholar
  12. A. Polyakov, JETP Lett. 20 (1974) 194Google Scholar
  13. P. Goddard, D. Olive, Rep. Prog. Phys. 41 (1978) 1357Google Scholar
  14. Goddard, D. Monopoles in Quantum Field Theory (eds N. Craigie, P. Goddard, W. Nahm, World Scientific, Singapore 1982).Google Scholar
  15. 5.
    M. Atiyah, I. Singer, Ann. Math 87 (1968) 485, 546CrossRefGoogle Scholar
  16. K. Fujikawa, Phys. Rev. D21 (1980) 2848.Google Scholar
  17. 6.
    J. Bell, R. Jackiw, Nuovo Cim. 60A (1969) 47Google Scholar
  18. S. Adler, Phys. Rev. 177 (1969) 2426Google Scholar
  19. B. Zumino, Y. Wu, A. Zee, Nucl. Phys. B239 (1984) 477CrossRefGoogle Scholar
  20. K. Huang, Quarks, Leptons and Gauge Fields ( World Scientific, Singapore 1982).Google Scholar
  21. 7.
    R. Musto, L. O’Raifeartaigh, A. Wipf, Phys. Lett. (in print)Google Scholar
  22. R. Blankenbecler, D. Boyanovsky, Phys. Rev. D31 (1985) 3234Google Scholar
  23. T. Jaroszewicz, Harvard Univ. Preprint 1986.Google Scholar
  24. 8.
    L. Alvarez-Gaumé, Comm. Math. Phys. 90 (1983) 161.CrossRefGoogle Scholar
  25. 9.
    R. Brandt, F. Neri, Nucl. Phys. B161 (1979) 253CrossRefGoogle Scholar
  26. S. Coleman, CERN Lecture Notes (1979)Google Scholar
  27. P. Goddard, D. Olive, Nucl. Phys. B19 (1981) 528CrossRefGoogle Scholar
  28. E. Weinberg, Nucl. Phys. B167 (1980) 500Google Scholar
  29. A. Balachandran et al. Phys. Rev. 29D (1984) 2919, 2936Google Scholar
  30. P. Horvâthy, L. O’Raifeartaigh, DIAS Preprint 1986.Google Scholar
  31. 10.
    M. Atiyah, R. Bott, Phil. Trans. R. Soc. Lond. A308 (1982) 523.Google Scholar
  32. 1l.
    P. Ramond, Field Theory, (Addison-Wesley,, MA 1981).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • L. O’Raifeartaigh
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublin 4Ireland

Personalised recommendations