# Thomas rotation and the parametrization of the Lorentz transformation group

@article{Ungar1988ThomasRA, title={Thomas rotation and the parametrization of the Lorentz transformation group}, author={Abraham Albert Ungar}, journal={Foundations of Physics Letters}, year={1988}, volume={1}, pages={57-89} }

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 well-knownThomas 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…

## 144 Citations

### Thomas rotation: a Lorentz matrix approach

- Physics
- 2002

The composition of two pure Lorentz transformations (boosts) parametrized by non-parallel velocities is equivalent to a boost combined with a pure spatial rotation - the Thomas rotation. Thirty years…

### Successive Lorentz transformations of the electromagnetic field

- Physics
- 1991

A velocity-orientation formalism to deal with compositions of successive Lorentz transformations, emphasizing analogies shared by Lorentz and Galilean transformations, has recently been developed.…

### The Quartet of Eigenvectors for Quaternionic Lorentz Transformation

- Physics
- 2020

In this paper the Lorentz transformation, considered as the composition of a rotation and a Lorentz boost, is decomposed into a linear combination of two orthogonal transforms. In this way a two-term…

### Graphical Representations for the Successive Lorentz Transformations. Application: Lorentz Contraction and Its Dependence on Thomas Rotation

- Physics
- 2016

A new vectorial representation for the successive Lorentz transformations (SLT) has recently been proved very convenient to achieve a straightforward treatment of the Thomas rotation effect. Such a…

### Einstein law of composition of three non-collinear velocities and its dependence on Thomas rotation: application to light aberration

- PhysicsEuropean Journal of Physics
- 2018

Two Cartesian forms and a vectorial one for the Einstein law of composition of three non-collinear velocities are obtained for the first time, and their dependence on the Thomas rotation angle is…

### Vectorial Form of the Successive Lorentz Transformations. Application: Thomas Rotation

- Physics
- 2012

A complete treatment of the Thomas rotation involves algebraic manipulations of overwhelming complexity. In this paper, we show that a choice of convenient vectorial forms for the relativistic…

### THE LORENTZ BOOST-LINK IS NOT UNIQUE. Relative velocity as a morphism in a connected groupoid category of null objects

- Mathematics
- 2006

The isometry-link problem is to determine all isometry transformations among given pair of vectors with the condition that if these initial and final vectors coincide, the transformation-link must be…

### From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups

- Physics
- 2016

The Lorentz transformation of order $(m=1,n)$, $ninNb$, is the well-known Lorentz transformation of special relativity theory. It is a transformation of time-space coordinates of the…

### Parametric Realization of the Lorentz Transformation Group in Pseudo-Euclidean Spaces

- Mathematics
- 2015

The Lorentz transformation group $SO(m,n)$ is a group of Lorentz transformations of order $(m,n)$, that is, a group of special linear transformations in a pseudo-Euclidean space of signature $(m,n)$…

### Successive Lorentz transformations for energy and momentum. Application: relativistic elastic scattering of two particles having non-collinear velocities and its dependence on Thomas rotation

- Physics
- 2021

Successive Lorentz transformations (SLT) for energy and momentum are derived, and the involved Thomas rotation angle (TRA) is highlighted. In particular, if the axes of the coordinate systems related…

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