Deformation Quantization of Odd Dimensional anti-de Sitter Spaces as Contact Manifolds

TL;DR

This paper presents a method to quantize odd-dimensional anti-de Sitter spaces by viewing them as contact manifolds and applying deformation quantization techniques, extending to general hypersurfaces defined by homogeneous functions.

Contribution

It introduces a novel approach to quantize odd-dimensional anti-de Sitter spaces using contact geometry and symplectization, generalizing to other hypersurfaces.

Findings

Quantization of odd-dimensional anti-de Sitter spaces as contact manifolds.

Extension of the method to hypersurfaces defined by homogeneous functions.

Generalization of the deformation quantization process for contact manifolds.

Abstract

We quantize odd dimensional anti-de Sitter spaces by applying the method of deforming contact manifolds proposed by Rajeev. The construction in the present paper consists of the identification of the odd dimensional anti-de Sitter space as a hypersurface of contact type and the subsequent use of 'symplectization' principle. We also show that this construction generalizes to any odd dimensional hypersurface which can be represented as a nonzero level set of a homogenous function.