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On free Lie algebras and particles in electro-magnetic fields

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arxiv 1705.05854 v2 pith:KM6UR2LX submitted 2017-05-16 hep-th

Joaquim Gomis , Axel Kleinschmidt This is my paper · ORCID
classification hep-th
keywords algebraalgebraselectro-magneticextensionsfreemaxwellsymmetryanalysed
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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.

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Cited by 5 Pith papers

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    Supersymmetric extensions of extended kinematical algebras are classified via semigroup expansion, and non-degenerate Chern-Simons supergravity actions are constructed in three dimensions.

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    New infinite-dimensional superalgebras, the deformed and enlarged super-BMS3 algebras for N=1,2,4, are produced by S-expanding super-Virasoro and are related by a flat limit.

  3. Boundary dynamics of Maxwell-invariant three-dimensional Chern-Simons gravity

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    A Maxwellian extension of flat Liouville theory is derived as the boundary dual of Maxwell-invariant 2+1 Chern-Simons gravity, and is shown to match a geometric action and a Carrollian expansion of the AdS3 dual.

  4. Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields

    hep-th 2024-12 conditional novelty 5.0 of 10

    The asymptotic symmetry algebra of three-dimensional Maxwell Chern-Simons gravity with spin-3 fields is a new nonlinear algebra, hs3max-bms3, which is also obtained as the flat limit of three copies of the W3 algebra.

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