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General Relativity and Gravitation

, Volume 19, Issue 6, pp 643–648 | Cite as

Spin substructure of space-time

  • Kaare Borchsenius
Research Articles

Abstract

Space-time is provided with an underlying SL(2,C) spin space with complex noncommutative spinor coordinatesC A which satisfy\(x^{\dot AB} = \tfrac{1}{2}\{ C^{\dot A} ,C^B \} \). It is shown that the orbital angular momentum operator has a realization in this space as a derivative operator which can take on half-integral spin values, and the graded Lie algebra which describes the structure of the spin space is discussed. The spin-space translations mix fermi and bose fields and produce space-time translations which are not nil-potent. A hermitean metric with a line element which is invariant under such localx-dependent translations is introduced.

Keywords

Angular Momentum Differential Geometry Line Element Orbital Angular Momentum Momentum Operator 
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.

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References

  1. 1.
    Fayet, P., and Ferrara, S. (1977).Phys. Rept.,32, 5, 249.Google Scholar
  2. 2.
    Infeld, L., and Van Der Waerden, B. L. (1933).Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 9, 380.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Kaare Borchsenius
    • 1
  1. 1.KlemenskerDenmark

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