Orbit method quantization of the AdS$_2$ superparticle

TL;DR

This paper develops a method to quantize the AdS2 superparticle using orbit method and Hamiltonian reduction, providing explicit canonical coordinates and quantization, with new insights into the massless case.

Contribution

It introduces a novel orbit method quantization approach for the AdS2 superparticle on the OSP(1|2)/SO(1,1) coset, including explicit canonical coordinates and analysis of massless case issues.

Findings

Canonical coordinates are constructed as bosonic and fermionic oscillators.

Quantization yields a Holstein-Primakoff type realization of osp(1|2).

New features and inconsistencies are identified in the massless superparticle case.

Abstract

We consider the Hamiltonian reduction and canonical quantization of a massive AdS$_2$ superparticle realized on the coset OSP(1|2)/SO(1,1). The phase space of the massive superparticle is represented as a coadjoint orbit of a timelike element of $\mathfrak{osp}$(1|2). This orbit has a well defined symplectic structure and the OSP(1|2) symmetry is realized as the Poisson bracket algebra of the Noether charges. We then construct canonical coordinates given by one bosonic and one fermionic oscillator, whose quantization leads to the Holstein-Primakoff type realization of $\mathfrak{osp}$(1|2). We also perform a similar analysis and discuss new features and inconsistencies in the massless case.