Relativistic Transformations. The Lorentz Group
Chapter
Abstract
A rotation1 may be specified by a vector, θ
, in such a way that (Fig. 1.1.1) the rotation axis lies along θ
, the rotation angle being θ = |θ|, and the direction of the rotation determined by the corkscrew rule. If we denote the rotation by R(θ
), it acts upon a vector r according to for θ
infinitesimal,
$$r \to r = R\left( \theta \right)r = \left( {\cos \theta } \right)r + \left( {1 - \cos \theta } \right)\frac{{\theta r}}{{\theta ^2 }}\theta + \frac{{\sin \theta }}{\theta }\theta \times r;$$
(1.1.1a)
$$R\left( \theta \right)r = r + \theta \times r + O\left( {\theta ^2 } \right).$$
(1.1.1b)
Keywords
Minkowski Space Lorentz Transformation Lorentz Group Relativistic Transformation Lorentz Boost
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 1996