Abstract
The covariant differential properties of the split Cayley subalgebra of local real quaternion tetrads is considered. Referred to this local quaternion tetrad several geometrical objects are given in terms of Zorn–Weyl matrices. Associated with a pair of real null vectors we define two-component spinor fields over the curved space and the associated Zorn–Weyl matrices which satisfy the Dirac equation written in terms of the Zorn algebra. The formalism is generalized by considering a field of complex tetrads defining a Hermitian second rank tensor. The real part of this tensor describes the gravitational potentials and the imaginary part the electromagnetic potentials in the Lorentz gauge. The motion of a charged spin zero test body is considered. The Zorn–Weyl algebra associated with this generalized formalism has elements belonging to the full octonion algebra.
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