Abstract
The Poincaré algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electromagnetic 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∞. A specific dynamical system with this infinite symmetry is constructed and analysed.
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Gomis, J., Kleinschmidt, A. On free Lie algebras and particles in electro-magnetic fields. J. High Energ. Phys. 2017, 85 (2017). https://doi.org/10.1007/JHEP07(2017)085
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DOI: https://doi.org/10.1007/JHEP07(2017)085