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A Relativistic Quaternionic Wave Equation

Charles Schwartz
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Abstract

We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved quantity which looks like helicity. The principle of superposition is retained in a slightly altered manner. External potentials can be introduced in a way that allows for gauge invariance. There are some results for scattering theory and for two-particle wavefunctions as well as the beginnings of second quantization. However, we are unable to find a suitable Lagrangian or an energy-momentum tensor.

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Charles Schwartz. 2006-09-21. A Relativistic Quaternionic Wave Equation. https://doi.org/10.1063/1.2397555

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