A Relativistic Quaternionic Wave Equation
High Energy Physics - Theory
2008-11-26 v4
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.
Cite
@article{arxiv.hep-th/0607121,
title = {A Relativistic Quaternionic Wave Equation},
author = {Charles Schwartz},
journal= {arXiv preprint arXiv:hep-th/0607121},
year = {2008}
}
Comments
19 pages; minor corrections in Section 11 and Appendix A