Coset construction of AdS particle dynamics

Abstract

We analyze the dynamics of the AdSN+1 particle realized on the coset SO(2, N)/SO (1,N). Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boosting a timelike element of 𝔰𝔬(2, N). We show equivalence of this approach to geometric quantization and to the SO(N) covariant oscillator description, for which the boost generators entail a complicated operator ordering. As an alternative scheme, we introduce dual oscillator variables and derive their algebra at the classical and the quantum levels. This simplifies the calculations of the commutators for the boost generators and leads to unitary irreducible representations of 𝔰𝔬(2, N) for all admissible values of the mass parameter. We furthermore discuss an SO(N) covariant supersymmetric extension of the oscillator quantization, with its realization for superparticles in AdS2 and AdS3 given by recent works.