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A Quaternion Representation of the Lorentz Group for Classical Physical Applications

TitleA Quaternion Representation of the Lorentz Group for Classical Physical Applications
Publication TypeJournal Article
Year of Publication1991
AuthorsAbonyi, I., J. Bitó, and J. K. Tar
JournalJOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume24
Pagination3245 - 3254
Date Published1991
Publication Languageeng
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.