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The triality properties of Dirac spinors are studied, including a construction of the algebra of (complexified) biquaternion. A bilinear law of composition for biquaternion is defined by means of Levi-civita symbol and Lorentzian metric only. It is proved that there exists a vector-representation of Dirac spinors. The massive Dirac equation in the vector-representation is actually self-dual. A chiral...
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