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A new formula for the exponents of the generators of the Lorentz group. (English) Zbl 1098.22008
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 98-115 (2006).
The level of this paper is quite elementary. The authors show that any matrix in the Lie algebra so$\left(3,1\right)$ of the Lorentz group SO$\left(3,1\right)$ can be mapped via an inner automorphism into a matrix which is of much simpler form. Then the authors obtain a formula for the exponent $expX$ of an arbitrary matrix $X$ in so$\left(3,1\right)$. As an application, the authors determine the trajectories of a particle with mass $m$ which carries an electric charge $e$ in a constant electromagnetic field specified by a matrix $X$ in so$\left(3,1\right)$.
##### MSC:
 22E43 Structure and representation of the Lorentz group 22E70 Applications of Lie groups to physics; explicit representations 70B05 Kinematics of a particle