Derives manifestly covariant worldline actions for Poincaré and AdS particles from symplectic forms on coadjoint orbits via Hamiltonian constraints from isometry conditions.
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In this note we have considered a relativistic Nambu-Goto model for a particle in $AdS$ metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed \cite{pal} "Exotic Oscillator". The Snyder algebra and subsequently the $\kappa$-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncommutative spacetime in the context of open string where only a curved target space is introduced.
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Ab Initio Construction of Poincar\'e and AdS Particle
Derives manifestly covariant worldline actions for Poincaré and AdS particles from symplectic forms on coadjoint orbits via Hamiltonian constraints from isometry conditions.