Notes on the BMS group in three dimensions: I. Induced representations

TL;DR

The paper develops a Mackey-style program for the BMS3 group, identifying induced representations with Virasoro coadjoint orbits and providing explicit one-particle realizations. It shows that, because BMS3 is a semidirect product with an adjoint action, the representation theory is governed by coadjoint data of the Virasoro group, yielding a detailed classification into massive, massless, and tachyonic sectors with continuous spin. Energy bounds are analyzed to distinguish physically acceptable (stable) representations, and the framework clarifies the particle content of three-dimensional flat-space gravity and its relation to Virasoro dynamics. The work sets the stage for a companion study of the coadjoint representation and opens questions about invariant measures and the completeness of the induced-representation program for  BMS3 and related algebras.

Abstract

The Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the circle with the space of its adjoint representation, embedded as an abelian normal subgroup. The structure of the group suggests to study induced representations; we show here that they are associated with the well-known coadjoint orbits of the Virasoro group and provide explicit representations in terms of one-particle states.