Notes on the BMS group in three dimensions: II. Coadjoint representation

TL;DR

This paper studies the coadjoint representation of the BMS$_3$ group in three-dimensional flat gravity, classifying orbits and clarifying angular momentum ambiguities, with implications for geometric quantization.

Contribution

It provides a detailed classification of coadjoint BMS$_3$ orbits and addresses the supertranslation ambiguity in angular momentum.

Findings

Intrinsic angular momentum is free of supertranslation ambiguities.

Coadjoint orbits are classified systematically.

Connection with induced representations and geometric quantization is discussed.

Abstract

The coadjoint representation of the BMS$_3$ group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS$_3$ orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, the link with induced representations upon geometric quantization is discussed.