Ab Initio Construction of Poincaré and AdS Particle

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.

19 pages, matching with the published version

References in corpus (6)

• Chiral fermions as classical massless spinning particles
• Scalar heat kernel with boundary in the worldline formalism
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• The worldline formalism in strong-field QED
• Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits