Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

TL;DR

This paper presents a method to quantize massive scalar particles in AdS spacetime using oscillator representations, leading to new realizations of the symmetry group SO(2,N) and its unitary irreducible representations.

Contribution

It introduces a novel oscillator quantization approach for scalar particles in AdS, providing explicit realizations of SO(2,N) representations across all unitarity ranges.

Findings

Explicit oscillator-based realizations of SO(2,N) UIRs.

Consistent deformation of classical symmetry generators during quantization.

Applicability to the entire unitarity range of minimal energy .

Abstract

The set of trajectories for massive spinless particles on $AdS_{N+1}$ spacetime is described by the dynamical integrals related to the isometry group SO(2,N). The space of dynamical integrals is mapped one to one to the phase space of the $N$-dimensional oscillator. Quantizing the system canonically, the classical expressions for the symmetry generators are deformed in a consistent way to preserve the $so(2,N)$ commutation relations. This quantization thus yields new explicit realizations of the spin zero positive energy UIR's of SO(2,N) for generic $N$. The representations as usual can be characterized by their minimal energy $\alpha$ and are valid in the whole range of $\alpha$ allowed by unitarity.