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Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,” Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, “Energetics of two-body Hamiltonians in post-Minkowskian gravity,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
A. Koemans Collado, P. Di Vecchia and R. Russo, “Revisiting the 2PM eikonal and the dynamics of binary black holes,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, “Post-Minkowskian Hamiltonians in general relativity,” Phys. Rev. D 100
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP 10
Original
1908
Earlier work this paper cites.
P. Di Vecchia, A. Luna, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, “A tale of two exponentiations in 𝒩 = 8 {\cal N}=8 supergravity,” Phys. Lett. B 798
Original
1908
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” JHEP 01
Original
1910
Earlier work this paper cites.
N. E. J. Bjerrum-Bohr, A. Cristofoli and P. H. Damgaard, “Post-Minkowskian Scattering Angle in Einstein Gravity,” JHEP 08
Original
1910
Earlier work this paper cites.
P. Di Vecchia, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, “A tale of two exponentiations in 𝒩 \mathcal{N} = 8 supergravity at subleading level,” JHEP 03
Original
1911
Earlier work this paper cites.
B. C. Eu, “On the WKB Approximation in Time-Dependent Scattering Theory Including Rearrangement Processes,” J. Chem. Phys. 57
1972
Earlier work this paper cites.
G. ’t Hooft, “Graviton Dominance in Ultrahigh-Energy Scattering,” Phys. Lett. B 198
1987
Earlier work this paper cites.
D. Amati, M. Ciafaloni, and G. Veneziano, “Superstring Collisions at Planckian Energies,” Phys. Lett. B197
1987
Earlier work this paper cites.
D. Amati, M. Ciafaloni and G. Veneziano, “Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions,” Int. J. Mod. Phys. A 3
1988
Earlier work this paper cites.
D. Amati, M. Ciafaloni and G. Veneziano, “Higher Order Gravitational Deflection and Soft Bremsstrahlung in Planckian Energy Superstring Collisions,” Nucl. Phys. B 347
1990
Earlier work this paper cites.

Similar

D. Amati, M. Ciafaloni and G. Veneziano, “Planckian scattering beyond the semiclassical approximation,” Phys. Lett. B 289
1992
Cited alongside, same era.
D. N. Kabat and M. Ortiz, “Eikonal quantum gravity and Planckian scattering,” Nucl. Phys. B 388
1992
Cited alongside, same era.
D. Amati, M. Ciafaloni and G. Veneziano, “Effective action and all order gravitational eikonal at Planckian energies,” Nucl. Phys. B 403
1993
Cited alongside, same era.
Z. Bern, H. Ita, J. Parra-Martinez and M. S. Ruf, “Universality in the classical limit of massless gravitational scattering,” Phys. Rev. Lett. 125
Original
2002
Cited alongside, same era.
A. Cristofoli, P. H. Damgaard, P. Di Vecchia and C. Heissenberg, “Second-order Post-Minkowskian scattering in arbitrary dimensions,” JHEP 07
Original
2003

Then

T. Damour, “High-energy gravitational scattering and the general relativistic two-body problem,” Phys. Rev. D 97
Original
2018
Later among the works it cites.
N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté and P. Vanhove, “General Relativity from Scattering Amplitudes,” Phys. Rev. Lett. 121
Original
2018
Later among the works it cites.
C. Cheung, I. Z. Rothstein and M. P. Solon, “From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion,” Phys. Rev. Lett. 121
Original
2018
Later among the works it cites.
A. K. Collado, P. Di Vecchia, R. Russo and S. Thomas, “The subleading eikonal in supergravity theories,” JHEP 1810
Original
2018
Later among the works it cites.
D. A. Kosower, B. Maybee and D. O’Connell, “Amplitudes, Observables, and Classical Scattering,” JHEP 02

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2021

On an Exponential Representation of the Gravitational S-Matrix

Damgaard, Poul H., Plante, Ludovic, Vanhove, Pierre

Understand

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes.

While sharing some similarities with the eikonal formalism it differs from it in details.
Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts.
Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms.

Built on

Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,” Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, “Energetics of two-body Hamiltonians in post-Minkowskian gravity,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
A. Koemans Collado, P. Di Vecchia and R. Russo, “Revisiting the 2PM eikonal and the dynamics of binary black holes,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, “Post-Minkowskian Hamiltonians in general relativity,” Phys. Rev. D 100
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP 10
Original
1908
Earlier work this paper cites.
P. Di Vecchia, A. Luna, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, “A tale of two exponentiations in 𝒩 = 8 {\cal N}=8 supergravity,” Phys. Lett. B 798
Original
1908
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” JHEP 01
Original
1910
Earlier work this paper cites.
N. E. J. Bjerrum-Bohr, A. Cristofoli and P. H. Damgaard, “Post-Minkowskian Scattering Angle in Einstein Gravity,” JHEP 08
Original
1910
Earlier work this paper cites.
P. Di Vecchia, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, “A tale of two exponentiations in 𝒩 \mathcal{N} = 8 supergravity at subleading level,” JHEP 03
Original
1911
Earlier work this paper cites.
B. C. Eu, “On the WKB Approximation in Time-Dependent Scattering Theory Including Rearrangement Processes,” J. Chem. Phys. 57
1972
Earlier work this paper cites.
G. ’t Hooft, “Graviton Dominance in Ultrahigh-Energy Scattering,” Phys. Lett. B 198
1987
Earlier work this paper cites.
D. Amati, M. Ciafaloni, and G. Veneziano, “Superstring Collisions at Planckian Energies,” Phys. Lett. B197
1987
Earlier work this paper cites.
D. Amati, M. Ciafaloni and G. Veneziano, “Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions,” Int. J. Mod. Phys. A 3
1988
Earlier work this paper cites.
D. Amati, M. Ciafaloni and G. Veneziano, “Higher Order Gravitational Deflection and Soft Bremsstrahlung in Planckian Energy Superstring Collisions,” Nucl. Phys. B 347
1990
Earlier work this paper cites.

Similar

D. Amati, M. Ciafaloni and G. Veneziano, “Planckian scattering beyond the semiclassical approximation,” Phys. Lett. B 289
1992
Cited alongside, same era.
D. N. Kabat and M. Ortiz, “Eikonal quantum gravity and Planckian scattering,” Nucl. Phys. B 388
1992
Cited alongside, same era.
D. Amati, M. Ciafaloni and G. Veneziano, “Effective action and all order gravitational eikonal at Planckian energies,” Nucl. Phys. B 403
1993
Cited alongside, same era.
Z. Bern, H. Ita, J. Parra-Martinez and M. S. Ruf, “Universality in the classical limit of massless gravitational scattering,” Phys. Rev. Lett. 125
Original
2002
Cited alongside, same era.
A. Cristofoli, P. H. Damgaard, P. Di Vecchia and C. Heissenberg, “Second-order Post-Minkowskian scattering in arbitrary dimensions,” JHEP 07
Original
2003