Accession Number:

AD0617799

Title:

ROTATIONS AND LORENTZ TRANSFORMATIONS,

Descriptive Note:

Corporate Author:

TEXAS UNIV AUSTIN DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1964-02-02

Pagination or Media Count:

18.0

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 Synges theorem. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE