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.

arXiv comment19 pages, matching with the published version

References in corpus (16)

• BMS Particles in Three Dimensions
• Chiral fermions as classical massless spinning particles
• A Universal Model of D=4 Spinning Particle
• A Geometric Model of Arbitrary Spin Massive Particle
• Scalar heat kernel with boundary in the worldline formalism
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• The $AdS$ particle
• Semidirect products and the Pukanszky condition
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Interaction Vertex for Classical Spinning Particles
• Massive Spinning Particle in Any Dimension I. Integer Spins
• The worldline formalism in strong-field QED
• Adjoint and coadjoint orbits of the Poincaré group
• A uniform model of the massive spinning particle in any dimension
• The Kirillov picture for the Wigner particle
• Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits