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Zbl 1098.22008
Dimitrov, Georgi K.; Mladenov, Iva\"ilo M.
A new formula for the exponents of the generators of the Lorentz group. (English)
[A] Mladenov, Iva\"ilo (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. 98-115 (2006). ISBN 954-8495-30-9/pbk

The level of this paper is quite elementary. The authors show that any matrix in the Lie algebra so$(3,1)$ of the Lorentz group SO$(3,1)$ 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 $\exp X$ of an arbitrary matrix $X$ in so$(3,1)$. 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$(3,1)$.
[Benjamin Cahen (Metz)]

MSC 2000:: *22E43 Structure and representation of the Lorentz group
22E70 Appl. of Lie groups to physics
70B05 Kinematics of particle

Keywords: Lorentz group; exponent of a matrix; trajectories of a particle

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