Classical theory of the octonian field

Abstract

We develop a nonassociative classical theory of the octonion spinor field. We construct the Lagrange function, the field equations, the solutions, the energymomentum tensor, the spin, and the associator, which is a new quantum characteristic. We consider the interaction of the octonion spinor field with the electromagnetic field. We show that, in the case of a massless field, the energy, the spin, and the associator can be measured simultaneously, while in the case of a field with rest mass, only either spin and energy or spin and associator can be measured simultaneously.