Abstract
Octonions, or Cayley numbers, are used to extract the square root of the classical relativistic Hamiltonian, in place of the usual Dirac matrices. The resulting wave equation, analogous to the usual Dirac equation, is found to be equivalent to a pair of coupled Dirac equations. Thus, the introduction of the octonion algebra in place of the Dirac algebra provides nothing new in principle within the context of linear relativistic wave equations.
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