Clifford and Dirac-Hestenes Spinor Fields

  • Waldyr Alves RodriguesJr
  • Edmundo Capelas de Oliveira
Part of the Lecture Notes in Physics book series (LNP, volume 722)


Vector Bundle Covariant Derivative Dirac Equation Dirac Operator Global Section 
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.
    Aharonov, Y. and Susskind, L., Observability of the Sign of Spinors under a 2π Rotation, Phys. Rev. 15, 1237-1238 (1967).CrossRefADSGoogle Scholar
  2. 2.
    Avis, S. J. and Isham, C. J., Generalized Spin Structures and Four Dimensional Space-Times, Commun. Math. Phys. 7, 103-118 (1980).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Been, I. M. and Tucker, R. W., Representing Spinors with Differential Forms, in Trautman, A. and Furlan, G. (eds.), Spinors in Physics and Geometry, World Scientific, Singapore, 1988.Google Scholar
  4. 4.
    Bismut, J. M., A Local Index Theorem for non Kähler Manifolds, Mat. Ann. 28, 681-699 (1989).CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bleecker, D., Gauge Theory and Variational Principles, Addison-Wesley Publ. Co., Inc., Reading, MA, 1981.zbMATHGoogle Scholar
  6. 6.
    Choquet-Bruhat, Y., DeWitt-Morette, C. and Dillard-Bleick, M., Analysis, Manifolds and Physics (revisited edition), North Holland Publ. Co., Amsterdam, 1982.zbMATHGoogle Scholar
  7. 7.
    Crumeyrolle, A., Orthogonal and Sympletic Clifford Algebras, Kluwer Acad. Publ., Dordrecht, 1990.Google Scholar
  8. 8.
    Dalakov, P. and Ivanov, S., Harmonic Spinors of the Dirac Operator of Connection with Torsion in Dimension Four, Class. Quant. Grav. 1, 253-263 (2001).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Frankel, T., The Geometry of Physics, Cambridge University Press, Cambridge, 1997.zbMATHGoogle Scholar
  10. 10.
    Friedrich, T., Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics, 2, Am. Math. Soc., Providence, Rhode Island, 2000.Google Scholar
  11. 11.
    Geroch, R. Spinor Structure of Space-Times in General Relativity I, J. Math. Phys. , 1739-1744 (1968).Google Scholar
  12. 12.
    Geroch, R. Spinor Structure of Space-Times in General Relativity. II, J. Math. Phys. 1, 343-348 (1970).CrossRefADSGoogle Scholar
  13. 13.
    Graf, W., Differential Forms as Spinors, Ann. Inst. Henri Poincaré XXIV, 85-109 (1978).MathSciNetGoogle Scholar
  14. 14.
    Kähler, E., Der Innere Differentialkalkül, Rendiconti di Matematica e delle sue Applicazioni 2, 425-523 (1962).Google Scholar
  15. 15.
    Lawson, H. Blaine, Jr. and Michelson, M. L., Spin Geometry, Princeton University Press, Princeton, 1989.zbMATHGoogle Scholar
  16. 16.
    Lichnerowicz, A., Spineurs Harmoniques, C. R. Acad. Sci. Paris Sér. A 257, 7-9 (1963).zbMATHMathSciNetGoogle Scholar
  17. 17.
    Lounesto, P., Clifford Algebras, Relativity and Quantum Mechanics, in P. Letelier and W. A. Rodrigues Jr. (eds.) Gravitation: The Spacetime Structure, 50–8, World Sci. Publ. Co., Singapore, 1994.Google Scholar
  18. 18.
    Milnor, J., Spin Structures on Manifolds, L’ Enseignement Mathématique , 198-203 (1963).Google Scholar
  19. 19.
    Mosna, R. A. and Rodrigues, W. A., Jr., The Bundles of Algebraic and Dirac-Hestenes Spinor Fields, J. Math. Phys. 4, 2945-2966 [math-ph/0212033]Google Scholar
  20. 20.
    Naber, G. L., Topology, Geometry and Gauge Fields. Interactions, Appl. Math. Sci. 141, Springer-Verlag, New York, 2000.zbMATHGoogle Scholar
  21. 21.
    Nakahara, M., Geometry, Topology and Physics, Institute of Physics Publ., Bristol and Philadelphia, 1990.zbMATHCrossRefGoogle Scholar
  22. 22.
    Nicolescu, L. I., Notes on Seiberg-Witten Theory, Graduate Studies in Mathematics 28, Am. Math. Soc., Providence, Rohde Island, 2000.Google Scholar
  23. 23.
    Oliveira, E. Capelas de, and Rodrigues, W. A. Jr., Dotted and Undotted Spinor Fields in General Relativity, Int. J. Mod. Phys. D 13, 1637-1659 (2004).zbMATHCrossRefADSGoogle Scholar
  24. 24.
    Osborn, H., Vector Bundles, vol. I, Acad. Press, New York, 1982.Google Scholar
  25. 25.
    Penrose, R. and Rindler W., Spinors and Spacetime, vol. 1, Cambridge University Press, Cambridge, 1986.Google Scholar
  26. 26.
    Ramond, P., Field Theory: A Modern Primer, Addison-Wesley Publ. Co., Inc., New York, 1989.Google Scholar
  27. 27.
    Rodrigues, W. A. Jr., Algebraic and Dirac-Hestenes Spinors and Spinor Fields, J. Math. Physics 45, 2908-2944 (2004). [math-ph/0212030]zbMATHCrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Waldyr Alves RodriguesJr
    • 1
  • Edmundo Capelas de Oliveira
    • 1
  1. 1.Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação CientíficaCampinasBrasil

Personalised recommendations