
Accession Number : AD0617799
Title : ROTATIONS AND LORENTZ TRANSFORMATIONS,
Corporate Author : TEXAS UNIV AUSTIN DEPT OF MATHEMATICS
Personal Author(s) : Rastall,Peter
Report Date : 02 FEB 1964
Pagination or Media Count : 18
Abstract : Any complex threedimensional rotation is determined by a complex vector and by a complex angle of rotation. New, short proofs are given of the homomorphisms between the threedimensional complex rotation group, the group of unimodular quaternions (or unimodular 2 X 2 matrices) and the restricted Lorentz group. A correspondence is established between certain complex threedimensional rotation vectors and twodimensional subspaces of Lorentz vectors. The twodimensional subspaces which are invariant under a given restricted Lorentz transformation are shown to be determined by those eigenvectors of the corresponding threedimensional rotation matrix which belong to real eigenvalues. For nonnull restricted Lorentz transformations this leads to a proof of Synge's theorem. (Author)
Descriptors : (*ROTATION, TRANSFORMATIONS(MATHEMATICS)), (*TRANSFORMATIONS(MATHEMATICS), MATRICES(MATHEMATICS)), (*RELATIVITY THEORY, TRANSFORMATIONS(MATHEMATICS)), GROUPS(MATHEMATICS), COMPLEX VARIABLES, VECTOR ANALYSIS
Distribution Statement : APPROVED FOR PUBLIC RELEASE