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

Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J.

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

Authors

Lukierski, J.

Stichel, P. C.

Zakrzewski, W. J.

Description

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.
LaTeX, 13 pages. V2: Section 4 shortened. The version in print in Physics Letters B