Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics
arXiv:math-ph/0309061 · doi:10.1088/0143-0807/24/4/357
Abstract
A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.
8 pages