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 Poincaré 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.
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Acknowledgments
We acknowledge interesting discussions with Luca Ciambelli, Miguel Campliglia, Jaume Gomis, Marc Henneaux, Axel Kleinschmidt and Sabrina Pasterski. JG acknowledges the hospitality of the Max Planck Albert Einstein Institute in Golm and the Perimeter Institute in Waterloo where this work has been completed. The work of CB is partially supported by Project MASHED (TED2021-129927B-I00), funded by MCIN/AEI/10.13039/501100011033 and by the European Union Next Generation EU/PRTR. JG has been supported in part by PID2019-105614GB-C21 and from the State Agency for Research of the Spanish Ministry of Science and Innovation through the Unit of Excellence Maria de Maeztu 2020-2023 award to the Institute of Cosmos Sciences (CEX2019-000918-M).
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Batlle, C., Campello, V. & Gomis, J. Particle realization of Bondi-Metzner-Sachs symmetry in 2 + 1 space-time. J. High Energ. Phys. 2023, 11 (2023). https://doi.org/10.1007/JHEP11(2023)011
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DOI: https://doi.org/10.1007/JHEP11(2023)011