Gravitation and Cosmology

, Volume 18, Issue 2, pp 100–103 | Cite as

Riemann-Cartan space in O-theory

  • V. Yu. DorofeevEmail author


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.


Dirac Equation Spinor Particle Lepton Sector Lorentz Violation Octonionic Algebra 
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  1. 1.
    P. Jordan. J. Neumann, and E. Wigner, On an Algebraic Generalization of the Quantum Mechanical Formalism, Ann. Math. 35, 29 (1934).CrossRefGoogle Scholar
  2. 2.
    V. A. Fock and D. D. Ivanenko, Géometrie quantique linéaire et déplacement paralléle, Comp. Rend. Acad. Sci. Paris 188, 1470 (1929).zbMATHGoogle Scholar
  3. 3.
    V. Yu. Dorofeev, Generalization of Lagrangian of Electro-weak Interaction to the Cayley Octaves Algebra, Izv. VUZov (Russia), Mathematics 11, 3 (2011); arxiv: 0908.3247.Google Scholar
  4. 4.
    V. Yu. Dorofeev, Construction of the Curvature on Cayley Algebra Octaves, Gipercomplexnye chisla v geometrii i fizike (Russia), 1 (5) 8, 117 (2011).Google Scholar
  5. 5.
    V. A. Kostelecky, N. Russell, and J. D. Tasson, Constraints on Torsion from Lorentz Violation, Phys. Rev. Lett. 100, 111102 (2008); arxiv: 0712.4393.ADSCrossRefGoogle Scholar
  6. 6.
    B. R. Heckel et al., Preferred-Frame and CPViolation Tests with Polarized Electrons, Phys. Rev. D. 78, 092006 (2008); arxiv: 0808.2673.ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.SPbSUEFSt. PetersburgRussia

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