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    Quaternion-Loop Quantum Gravity
    with S. S. E. Almeida Silva and F. S. Carvalho
    Foundations of Physics 39 (11): 1273-1279. 2009.
    It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a justification for quaternion quantum gravity at the Tev energy scale