Global constants in (2+1)--dimensional gravity

TL;DR

This paper reviews the algebra of global constants of motion in 2+1 dimensional gravity with negative cosmological constant, expressing them through spinors and gamma matrices, highlighting their quantum properties.

Contribution

It introduces a complete set of 10 global constants in 2+1 gravity using spinor and gamma matrix formalism, linking holonomy parameters to quantum commutators.

Findings

Global constants form a complete algebra in 2+1 gravity.

Holonomy parameters are represented as spinor components.

Quantum commutators relate to spinor norms.

Abstract

The extended conformal algebra (so)(2,3) of global, quantum, constants of motion in 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant is reviewed. It is shown that the 10 global constants form a complete set by expressing them in terms of two commuting spinors and the Dirac gamma matrices. The spinor components are the globally constant holonomy parameters, and their respective spinor norms are their quantum commutators.