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Abstract: We study the construction of a manifestly covariant worldline action from a coadjoint orbit. A coadjoint orbit is a submanifold in the dual vector space of a Lie algebra, generated by coadjoint actions. Since a coadjoint orbit is a symplectic space, we derive the worldline particle action from the symplectic two-form. One subtlety in formulating worldline particle actions from coadjoint orbits is the choice of a coordinate system that clearly illustrates physical properties of the particles. We introduce Hamiltonian constraints derived from the defining conditions of the isometry. This allows us to write a manifestly covariant worldline action. We demonstrate our method for both massive and massless particles in Minkowski and AdS spacetime.

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