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 three-dimensional rotation is determined by a complex vector and by a complex angle of rotation. New, short proofs are given of the homomorphisms between the three-dimensional 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 three-dimensional rotation vectors and two-dimensional 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 three-dimensional rotation matrix which belong to real eigenvalues. For non-null 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