Specific properties and spatial symmetry group of nonassociative spinor field

Abstract

On the basis of nonassociative spinor field theory, the specific properties of a nonassociative spinor field are investigated. A new quantum number is introduced: the associator, which is a measure of the nonassociativeness of the field. To calculate the associator and spin in nonassociative algebra, open and closed products are introduced. It is shown that the spin consists of two components: the first half (calculated by the open-product rule) is similar to ordinary spin, while the second half (calculated by the closed-product rule) is attributed to the associator, i.e., is related to shear in the auxiliary isotopic space. The associator basis is expanded to a complete octonion basis, and the Poincaré group of four-dimensional space is expanded to a Poincaré group of eight-dimensional space. It is shown that, from these generators, in the particle rest system, the nonzero independent eigenvalues are: one, the sign of the particle energy, one of the spin components, one of the associator spatial components, and c₇.