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On free Lie algebras and particles in electro-magnetic fields

  • Joaquim Gomis
  • Axel KleinschmidtEmail author
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Global Symmetries Space-Time Symmetries Sigma Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Departament de Fısica Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB)Universitat de BarcelonaBarcelonaSpain
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany
  3. 3.International Solvay InstitutesBrusselsBelgium

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