  In this paper we represent the generalization of relativistic quantum
mechanics on the base of eght-component values "octons", generating associative
noncommutative spatial algebra. It is shown that the octonic second-order
equation for the eight-component octonic wave function, obtained from the
Einshtein relation for energy and momentum, describes particles with spin of
1/2. It is established that the octonic wave function of a particle in the
state with defined spin projection has the specific spatial structure in the
form of octonic oscillator with two spatial polarizations: longitudinal linear
and transversal circular. The relations between bispinor and octonic
descriptions of relativistic particles are established. We propose the
eight-component spinors, which are octonic generalisation of two-component
Pauli spinors and four-component Dirac bispinors. It is shown that proposed
eight-component spinors separate the states with different spin projection,
different particle-antiparticle state as well as different polarization of the
octonic oscillator. We demonstrate that in the frames of octonic relativistic
quantum mechanics the second-order equation for octonic wave function can be
reformulated in the form of the system of first-order equations for quantum
fields, which is analogous to the system of Maxwell equations for the
electromagnetic field. It is established that for the special type of wave
functions the second-order equation can be reduced to the single first-order
equation, which is analogous to the Dirac equation. At the same time it is
shown that this first-order equation describes particles, which do not create
quantum fields.
