Abstract
We represent sixteen-component values "sedeons," generating associative noncommutative space–time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space–time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space–time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.
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