Algebraic structure of nonassociative spinor field

An analysis of the algebra of octonions, the algebraic structure of nonassociative spinors, is presented, and a spinor field theory that is completely identical to Dirac theory is constructed in an associative basis. A spinor covariance transformation is introduced, and it is shown that it coincides with the Poincaré group of 4-dimensional space. The field equation is introduced through a spinor invariance transformation. Constraints imposed by the field equation on the eigenvalues of the transformation generators are considered. It is proved that the particles in a system at rest which are nonzero are , the unit; , the energysign of the particle; and s ₆, one of the spin components of the particle. Tbilisi University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 59–65, November, 1998.