Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity

Abstract

In this paper we derive an expression for the conserved Pauli-Lubanski scalar in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point particles. We find that it is represented by an extra spatial shift $\Delta$ in addition to the usual identification rule (being a rotation over the cut). For two particles this invariant is expressed in terms of 't Hooft's phase-space variables and we check its classical limit.

Some errors are corrected and a new introduction and discussion are added. 6 pages Latex, 4 eps-figures

References in corpus (1)

• Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions

Cited by in corpus (2)

• The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
• Winding Solutions for the two Particle System in 2+1 Gravity