A quaternion representation of the Lorentz group for classical physical applications

Abstract

A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.