Here, in this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.
Chatterjee, Atreya and Lowe, David A.. "BMS symmetry, soft particles and memory." Classical and Quantum Gravity, vol. 35, no. 9, Mar. 2018. https://doi.org/10.1088/1361-6382/aab5cc
Chatterjee, Atreya, & Lowe, David A. (2018). BMS symmetry, soft particles and memory. Classical and Quantum Gravity, 35(9). https://doi.org/10.1088/1361-6382/aab5cc
Chatterjee, Atreya, and Lowe, David A., "BMS symmetry, soft particles and memory," Classical and Quantum Gravity 35, no. 9 (2018), https://doi.org/10.1088/1361-6382/aab5cc
@article{osti_2340804,
author = {Chatterjee, Atreya and Lowe, David A.},
title = {BMS symmetry, soft particles and memory},
annote = {Here, in this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.},
doi = {10.1088/1361-6382/aab5cc},
url = {https://www.osti.gov/biblio/2340804},
journal = {Classical and Quantum Gravity},
issn = {ISSN 0264-9381},
number = {9},
volume = {35},
place = {United States},
publisher = {IOP Publishing},
year = {2018},
month = {03}}
Bondi, Hermann; Van der Burg, M. G. J.; Metzner, A. W. K.
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 269, Issue 1336, p. 21-52https://doi.org/10.1098/rspa.1962.0161
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 270, Issue 1340, p. 103-126https://doi.org/10.1098/rspa.1962.0206