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

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.

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

References in corpus (12)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• The exotic Galilei group and the "Peierls substitution"
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• On Schrödinger superalgebras
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Enlarged Galilean symmetry of anyons and the Hall effect
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Deformed Schrodinger symmetry on noncommutative space

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