Thomas rotation and the parametrization of the Lorentz transformation group
Abstract
Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the wellknown Thomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, wellknown Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final timelike 4vector.
 Publication:

Foundations of Physics Letters
 Pub Date:
 March 1988
 DOI:
 10.1007/BF00661317
 Bibcode:
 1988FoPhL...1...57U
 Keywords:

 Special theory of relativity;
 Lorentz transformation;
 parametrization;
 Thomas rotation