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

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.

Version accepted for publication in PRD. Expanded title and expanded discussion about superrotations in the massive case

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• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Detector Operators for Celestial Symmetries
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• Non Local Global Symmetries of a Free Scalar Field in a Bounded Domain
• BMS in higher space-time dimensions and Non-relativistic BMS