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On free Lie algebras and particles in electro-magnetic fields

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1705.05854.pdf
(Preprint), 307KB

JHEP07(2017)085.pdf
(Publisher version), 363KB

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Citation

Gomis, J., & Kleinschmidt, A. (2017). On free Lie algebras and particles in electro-magnetic fields. Journal of high energy physics: JHEP, 2017(07): 085. doi:10.1007/JHEP07(2017)085.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-8CC1-C
Abstract
The Poincar\'e algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the presence of multipoles. We point out a relation of this construction to free Lie algebras that gives a unified description of all possible kinematic extensions, leading to a symmetry algebra that we call Maxwell${}_\infty$. A specific dynamical system with this infinite symmetry is constructed and analysed.