UC Berkeley

We study a one-component quaternionic wave equation which is relativistically covariant. Bilinear forms include a conserved four-vector 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 wave functions as well as the beginnings of second quantization. However, we are unable to find a suitable Lagrangian or an energy-momentum tensor. (c) 2006 American Institute of Physics.