nLab soft graviton theorem

Idea

In perturbative quantum gravity, the soft graviton theorem (Weinberg 65) re-formulates scattering amplitudes of a set of finite energy external particles with one or more low energy external gravitons, in terms of the amplitude without the low energy gravitons.

In the classical limit, there is a different manifestation of the same theorem (Saha-Sahoo-Sen 19): here it determines the low frequency component of the gravitational wave-form produced during a scattering process in terms of the momenta and spin of the incoming and outgoing objects, without any reference to the interactions responsible for the scattering.

References

Original reference:

• Steven Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965) (doi:10.1103/PhysRev.140.B516)

Review with focus on photons in electromagnetism:

• Noah Miller, From Noether’s Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems (arXiv:2112.05289)

Exposition:

• Ashoke Sen: Gravitational Wave Tails from Soft Theorem: A Short Review [arXiv:2408.08851]

See also:

• Martin Beneke, Patrick Hager, Robert Szafron, Soft-Collinear Gravity and Soft Theorems, in section Effective Quantum Gravity of Handbook of Quantum Gravity, Springer (2023) [arXiv:2210.09336]

Discussion of application to gravitational waves in the classical limit:

• Arnab Priya Saha, Biswajit Sahoo, Ashoke Sen, Proof of the Classical Soft Graviton Theorem in $D=4$ (arXiv:1912.06413)

Discussion in the BFSS matrix model:

• Noah Miller, Andrew Strominger, Adam Tropper, Tianli Wang, Soft Gravitons in the BFSS Matrix Model [arXiv:2208.14547]

• Adam Tropper, Tianli Wang, Lorentz Symmetry and IR Structure of The BFSS Matrix Model [arXiv:2303.14200]

• Aidan Herderschee, Juan Maldacena, Soft Theorems in Matrix Theory [arXiv:2312.15111]

Analogous discussion for gluons:

• Peng Cheng, Pujian Mao, Soft gluon theorems in curved spacetime [arXiv:2211.00031]

Analogous discussion for phonons:

• Clifford Cheung, Maria Derda, Andreas Helset, Julio Parra-Martinez: Soft Phonon Theorems, J. High Energ. Phys. 2023 103 (2023) [arXiv:2301.11363, doi:10.1007/JHEP08(2023)103]