Particle realization of Bondi-Metzner-Sachs symmetry in 2+1 space-time

TL;DR

This paper develops a Lorentz invariant massive particle model in (2+1) dimensions that incorporates BMS symmetries, analyzing its Hamiltonian structure, gauge constraints, and massless limit, revealing residual BMS symmetries.

Contribution

It introduces a novel particle model in (2+1) dimensions with BMS symmetries using non-linear realization, and analyzes its Hamiltonian and gauge structure, including the massless limit.

Findings

Residual BMS symmetries in the reduced phase space

Massless limit includes superrotations

Hamiltonian formalism with gauge constraints

Abstract

We construct a Lorentz invariant massive particle model in (2+1) space-time with an enlarged set of symmetries which includes Bondi-Metzner-Sachs (BMS) translations (supertranslations), using the non-linear realization framework. The Hamiltonian formalism for the resulting Lagrangian is constructed, and the infinite phase-space constraints and the set of gauge transformations are analysed. We also compute the massless limit of the theory in phase-space. After eliminating the gauge degrees of freedom, the physical reduced space is left only with the degrees of freedom of a standard Poincar\'e particle but with a residual set of symmetries that we prove to be BMS. A similar result for the massless limit, including in this case superrotations, is pointed out.