Advertisement

International Journal of Theoretical Physics

, Volume 51, Issue 8, pp 2559–2563 | Cite as

On the Integrability Conditions for Infeld-Van der Waerden Spin-Affine Connexions

  • J. G. Cardoso
Article

Abstract

The integrability condition that must be formally fulfilled by any Infeld-Van der Waerden spin-affine connexion is derived explicitly. Some geometric properties of the action of torsionless covariant-derivative commutators on arbitrary spin tensors and densities are then brought out. The relevant calculations supply a set of new differential expressions which will presumably ensure the consistency of any formulation that involves utilizing normally the traditional two-component spinor methods for classical general relativity.

Keywords

Spin-affine connexions Infeld-Van der Waerden formalisms Integrability conditions 

References

  1. 1.
    Schrödinger, E.: Space-Time Structure. Cambridge University Press, Cambridge (1963) Google Scholar
  2. 2.
    Infeld, L., Van der Waerden, B.L.: Sitzber. Preuss. Akad. Wiss., Physik-Math. Kl. 9, 380 (1933) Google Scholar
  3. 3.
    Bade, W.L., Jehle, H.: Rev. Mod. Phys. 3(25), 714 (1953) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Cardoso, J.G.: Czechoslov. J. Phys. 4(55), 401 (2005) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Cardoso, J.G.: Acta Phys. Pol. B 8(38), 2525 (2007) MathSciNetADSGoogle Scholar
  6. 6.
    Cardoso, J.G.: Nuovo Cimento B 6(124), 631 (2009) MathSciNetADSGoogle Scholar
  7. 7.
    Kuerten, A.M., Cardoso, J.G.: Int. J. Theor. Phys. 50(10), 3007 (2011) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Cardoso, J.G.: The classical two-component spinor formalisms for general relativity I. Adv. Appl. Clifford Algebras (2012) (to appear) Google Scholar
  9. 9.
    Cardoso, J.G.: The classical two-component spinor formalisms for general relativity II. Adv. Appl. Clifford Algebras (2012) (to appear) Google Scholar
  10. 10.
    Schouten, J.A.: Z. Phys. 84, 92 (1933) ADSCrossRefGoogle Scholar
  11. 11.
    Schouten, J.A.: Indag. Math. 11, 178, 217, 336 (1949) Google Scholar
  12. 12.
    Schouten, J.A.: Ricci Calculus. Springer, Berlin, Göttingen, Heidelberg (1954) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsCentre for Technological Sciences-UDESCJoinvilleBrazil

Personalised recommendations