'4+6'-decomposition of ten-dimensional octonionic spinor wave equations and derivation of four-dimensional massless Dirac equations

A method of decomposition into external four dimensions and internal six dimensions of the wave equations of octonionic spinors in ten dimensions is given. To obtain the spinor wave equations in the external four-dimensional Minkowski space-time, octonions in the extra internal six dimensions are described. The zero-mode solutions of the extra six-dimensional octonionic wave equations are also argued, and the Dirac equations in the four-dimensional Minkowski space-time are derived. Moreover, a possibility of the chiral asymmetric fermions in four dimension is investigated