Advertisement

The Hidden Geometrical Nature of Spinors

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

Keywords

Division Algebra Simple Algebra Division Ring Dirac Spinor Primitive Idempotent 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aharonov, Y. and Susskind, L., Observability of the Sign of Spinors under a 2π Rotation, Phys. Rev. 158, 1237-1238 (1967).CrossRefADSGoogle Scholar
  2. 2.
    Ahluwalia-Khalilova, D. V., and Grumiller D., Spin Half Fermions, with Mass Dimension One: Theory, Phenomenology, and Dark Matter, JCAP 07, 012 (2005). [hep-th/0412080]ADSGoogle Scholar
  3. 3.
    Benn, I. M., and Tucker, R. W., An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol, 1987.Google Scholar
  4. 4.
    Bjorken, J. D., A Dynamical Origin for the Electromagnetic Field, Ann. Phys.(New York) 24, 174-187 (1963).CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Chevalley, C., The Algebraic Theory of Spinors and Clifford Algebras, Springer-Verlag, Berlin, 1997.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.Google Scholar
  7. 7.
    Crawford, J., On the Algebra of Dirac Bispinor Densities: Factorization and Inversion Theorems, J. Math. Phys. 26, 1439-1441 (1985).CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Crumeyrolle, A., Orthogonal and Sympletic Clifford Algebras, Kluwer Acad. Publ., Dordrecht, 1990.Google Scholar
  9. 9.
    Figueiredo, V. L., Rodrigues, W. A., Jr., and Oliveira, E. Capelas de, Covariant, Algebraic and Operator Spinors, Int. J. Theor. Phys. 29, 371-395 (1990).zbMATHCrossRefGoogle Scholar
  10. 10.
    Figueiredo, V. L., Rodrigues, W. A. Jr., and Oliveira, E. Capelas de., Clifford Algebras and the Hidden Geometrical Nature of Spinors, Algebras, Groups and Geometries 7, 153-198 (1990).zbMATHMathSciNetGoogle Scholar
  11. 11.
    Lawson, H. Blaine, Jr. and Michelson, M. L., Spin Geometry, Princeton University Press, Princeton, 1989.zbMATHGoogle Scholar
  12. 12.
    Lounesto, P., Clifford Algebras and Hestenes Spinors, Found. Phys. 23, 1203-1237 (1993).CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Lounesto, P., Clifford Algebras, Relativity and Quantum Mechanics, in Letelier and W. A. Rodrigues Jr. (eds.) Gravitation: The Spacetime Structure, 50–81, World Sci. Publ. Co., Singapore, 1994.Google Scholar
  14. 14.
    Lounesto, P., Clifford Algebras and Spinors, Cambridge Univ. Press, Cambridge,1997.zbMATHGoogle Scholar
  15. 15.
    Lounesto, P., Scalar Product of Spinors and an Extension of the Brauer-Wall Groups, Found. Phys. 11, 721-740 (1981).CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Miller, W., Jr., Symmetry Groups and their Applications, Academic Press, New York, 1972.zbMATHGoogle Scholar
  17. 17.
    Mosna, R. A., Miralles, D., and Vaz, J., Jr., Multivector Dirac Equations and Z2-Gradings Clifford Algebras, Int. J. Theor. Phys. 41, 1651-1671 (2002).zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Mosna, R. A., Miralles, D., and Vaz, J., Jr., Z2-Gradings on Clifford Algebras and Multivector Structures, J. Phys. A: Math. Gen. 36, 4395-4405 (2003). [math-ph/0212020]zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Porteous, I. R., Topological Geometry, second edition, Cambridge Univ. Press, Cambridge, 1981.zbMATHCrossRefGoogle Scholar
  20. 20.
    Porteous, I. R., Clifford Algebras and the Classical Groups, second edition, Cambridge Univ. Press, Cambridge, 2001.Google Scholar
  21. 21.
    Rodrigues, W. A. Jr., Algebraic and Dirac-Hestenes Spinors and Spinor Fields, J. Math. Physics 45, 2908-2944 (2004). [math-ph/0212030]zbMATHCrossRefADSGoogle Scholar
  22. 22.
    da Rocha, R., and Rodrigues, W.A. Jr., Where are ELKO Spinor Field in Lounesto Spinor Field Classification?, Mod. Phys. Lett. A, 21, 65-76 (2006). [math-phys/0506075]zbMATHCrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Zeni, J. R. R. and Rodrigues, W. A., Jr., A Thoughtful Study of Lorentz Transformations by Clifford Algebras, Int. J. Mod. Phys. A 7, 1793-1817 (1992).zbMATHCrossRefADSMathSciNetGoogle 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