# Canonical Realization of (2+1)-dimensional Bondi-Metzner-Sachs symmetry

## TL;DR

This paper constructs canonical realizations of the ms_3 algebra as symmetries of a free Klein-Gordon field in 2+1 dimensions, including supertranslations and superrotations, with both on-shell and off-shell formulations.

## Contribution

It provides explicit on-shell and off-shell realizations of ms_3 symmetry for scalar fields in 2+1 dimensions, detailing the associated Noether charges.

## Key findings

- Realizations include both supertranslations and superrotations.
- Constructed explicit Noether charges for the symmetries.
- Applicable to both massive and massless Klein-Gordon fields.

## Abstract

We construct canonical realizations of the $\mathfrak{bms}_3$ algebra as symmetry algebras of a free Klein-Gordon (KG) field in $2+1$ dimensions, for both the massive and massless case. We consider two types of realizations, one on-shell, written in terms of the Fourier modes of the scalar field, and the other one off-shell with non-local transformations written in terms of the KG field and its momenta. These realizations contain both supertranslations and superrotations, for which we construct the corresponding Noether charges.