Complex Orthogonal and Antiorthogonal Representation of Lorentz Group

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Abstract
By using the fact that a plane electromagnetic wave is described by two Lorentz invariant statements, a complex orthogonal representation of the Lorentz group, including charged fields, is discussed. The representation provides the possibility of a combined study of the P, C, T symmetry operations for spin ½ and spin 1 fields. In particular, the chargelessness of the neutrino as a complex fermion field results from a reducible three charge states representation of the complex group.