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Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations

J. Lukierski·P. C. Stichel·W. J. Zakrzewski
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Abstract

We add to Galilean symmetries the transformations describing constant accelerations. The corresponding extended Galilean algebra allows, in any dimension $D=d+1$, the introduction of one central charge $c$ while in $D=2+1$ we can have three such charges: c, θand θ'. We present nonrelativistic classical mechanics models, with higher order time derivatives and show that they give dynamical realizations of our algebras. The presence of central charge $c$ requires the acceleration square Lagrangian term. We show that the general Lagrangian with three central charges can be reinterpreted as describing an exotic planar particle coupled to a dynamical electric and a constant magnetic field.

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J. Lukierski, P. C. Stichel, W. J. Zakrzewski. 2007-04-25. Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations. https://doi.org/10.1016/j.physletb.2007.04.058

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