Riemann-Cartan space in O-theory

V.Yu. Dorofeev1


The O-theory Lagrangian, obtained as a generalization of the weak interaction Lagrangian SU(2) ×U(1) to the octonionic algebra, is analyzed. It is shown that whenever the model is chiral, it inevitably leads to the Riemann-Cartan space. The torsion on the Earth's surface is calculated. A comparison between the obtained value and the available empirical data is presented. Furthermore, it is inferred that the effect of torsion is small but cumulative.


  1. V. A. Kostelecky, N. Russell, and J. D. Tasson, Constraints on Torsion from Lorentz Violation. Phys. Rev. Lett. 100, 111102 (2008), arxiv: 0712.4393.
  2. B. R. Heckel et el., Preferred-Frame and CP-Violation Tests with Polarized Electrons. Phys. Rev. D. 78, 092006 (2008), arxiv: 0808.2673.
  3. V. Yu. Dorofeev, Construction of the curvature on Cayley algebra octaves. Gipercomplexnye chisla b geometrii i fizike (Russia), 1 (5) 8, 117-142 (2011).
  4. V. Yu. Dorofeev, Generalization of Lagrangian of electro-weak interaction to the Cayley octaves algebra. Izv. VUZov (Russia), Mathematics, 11, 3-12 (2011); arxiv: 0908.3247.
  5. V. A. Fock and D. D. Ivanenko, Geometrie quantique lineaire et deplacement parallele, Comp. Rend. Acad. Sci. Paris 188, 1470-1472 (1929).
  6. P. Jordan. J. Neumann, and E. Wigner, On an algebraic generalization of the quantum mechanical formalism. Ann. Math. 35, 29-64 (1934).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page