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Relativistic Quaternionic Wave Function


We study a one-component quaternionic wave equation which is relativisticallycovariant. Bilinear forms include a conserved four-vector current and an antisymmetricsecond rank tensor. Waves propagate within the light cone and there is aconserved quantity which looks like helicity. The principle of superposition is retainedin a slightly altered manner. External potentials can be introduced in a waythat allows for gauge invariance. There are some results for scattering theory andfor two-particle wave functions as well as the beginnings of second quantization.However, we are unable to find a suitable Lagrangian or an energy-momentumtensor.

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