General Relativity and Gravitation

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

Spin substructure of space-time

  • Kaare Borchsenius
Research Articles


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.


Angular Momentum Differential Geometry Line Element Orbital Angular Momentum Momentum Operator 
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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Kaare Borchsenius
    • 1
  1. 1.KlemenskerDenmark

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