Abstract
Non-associative classical field theory is set up on the basis of octonions. Algebra and projection operators of octonions, transformational properties of their elements regarding the Lorentz group are studied. Lorentz spinors and vectors have been determined through octonions. Lorentz invariants, Lagrangian function and equations of octonions field, their solutions, the Hamiltonian and spin vector have been obtained. A new non-associative quantum number, the associator, is introduced and its value for Lorentz spinors and tensors has been determined. Global and local symmetries of octonion fields equation and appropriate currents are studied, the problems of hydrogen atom and the possibilities of perturbation theory evolution are considered. It is indicated that the non-associative classical field theory in principle involves the basic results of Dirac theory along with new results.
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