ROTATIONS AND LORENTZ TRANSFORMATIONS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 02, 1964
- Accession Number
- AD0617799
Entities
People
- Peter Rastall
Organizations
- University of Texas at Austin