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# Accession Number:

## AD0617799

# Title:

## ROTATIONS AND LORENTZ TRANSFORMATIONS,

# Descriptive Note:

# Corporate Author:

## TEXAS UNIV AUSTIN DEPT OF MATHEMATICS

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#