https://doi.org/10.1140/epjc/s10052-025-15091-z
Review
Lectures on the Bondi–Metzner–Sachs Group and related topics in infrared physics
Center for Natural and Human Sciences, Federal University of ABC, Avenida dos Estados 5001, Bangú, Santo André, 09280-560, São Paulo, Brazil
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https://ror.org/028kg9j04
Received:
30
April
2025
Accepted:
20
November
2025
Published online:
11
May
2026
Abstract
These are the extended lecture notes for a minicourse presented at the I São Paulo School on Gravitational Physics discussing the Bondi–Metzner–Sachs (BMS) group, the group of symmetries at null infinity on asymptotically flat spacetimes. The BMS group has found many applications in classical gravity, quantum field theory in flat and curved spacetimes, and quantum gravity. These notes build the BMS group from its most basic prerequisites (such as group theory, symmetries in differential geometry, and asymptotic flatness) up to modern developments. These include its connections to the Weinberg soft graviton theorem, the memory effect, its use to construct Hadamard states in quantum field theory in curved spacetimes, and other ideas. Advanced sections briefly discuss the main concepts behind the infrared triangle in electrodynamics, superrotations, and the Dappiaggi–Moretti–Pinamonti group in expanding universes with cosmological horizons. New contributions by the author concerning asymptotic (conformal) Killing horizons are discussed at the end.
This work ©2025 by Níckolas de Aguiar Alves is licensed under Creative Commons Attribution 4.0 International.
Cover: perturbative diagrams used in the proof of Weinberg’s soft graviton theorem [234], discussed on Sect. 6.4.
© The Author(s) 2026
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