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We construct a Lorentz invariant massive particle model in (2+1) space-timewith 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 theinfinite phase-space constraints and the set of gauge transformations areanalysed. We also compute the massless limit of the theory in phase-space.After eliminating the gauge degrees of freedom, the physical reduced space isleft only with the degrees of freedom of a standard Poincar\'e particle butwith a residual set of symmetries that we prove to be BMS. A similar result forthe massless limit, including in this case superrotations, is pointed out.

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