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.
I. L. Buchbinder, M. V. Khabarov, T. V. Snegirev and Yu. M. Zinoviev, Lagrangian formulation of the massive higher spin N=1 supermultiplets in A d S 4 AdS_{4} space , Nucl. Phys. B942
Original
1901
Earlier work this paper cites.
Y. F. Bautista and A. Guevara, From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems , 1903.12419
Original
1903
Earlier work this paper cites.
W. Cho and K. Lee, Heterotic Kerr-Schild Double Field Theory and Classical Double Copy , JHEP 07
Original
1904
Earlier work this paper cites.
M. Carrillo Gonzalez, B. Melcher, K. Ratliff, S. Watson and C. D. White, The classical double copy in three spacetime dimensions , 1904.11001
Original
1904
Earlier work this paper cites.
A. Brandhuber and G. Travaglini, On higher-derivative effects on the gravitational potential and particle bending , 1905.05657
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, On Post-Minkowskian Hamiltonians in General Relativity , 1906.01579
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes , 1906.09260
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes , 1906.10071
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y.-t. Huang and D. O’Connell, Kerr Black Holes as Elementary Particles , 1906.10100
Original
1906
Earlier work this paper cites.
J. Plefka, C. Shi, J. Steinhoff and T. Wang, Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO , 1906.05875
Original
1906
Earlier work this paper cites.
M. M. Anber, Self-conjugate QCD , 1906.10315
Original
1906
Earlier work this paper cites.
A. Ochirov and B. Page, Multi-Quark Colour Decompositions from Unitarity , 1908.02695
Original
1908
Earlier work this paper cites.
Z. Bern, C. Boucher-Veronneau and H. Johansson, N ≥ \geq 4 Supergravity Amplitudes from Gauge Theory at One Loop , Phys.Rev. D84
Original
1935
Earlier work this paper cites.
F. J. Belinfante, On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields , Physica 7
1940
Earlier work this paper cites.
L. Rosenfeld, Sur le tenseur D’Impulsion-Energie , Acad. Roy. Belg. Memoirs de Classes de Science 18
1940
Earlier work this paper cites.
L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case , Phys. Rev. D9
1974
Earlier work this paper cites.
L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 2. The fermion case , Phys. Rev. D9
1974
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields , vol. 2 of Course of Theoretical Physics . Pergamon Press, Oxford, 1975
1975
Earlier work this paper cites.
J. F. Luciani, Coupling of O(2) Supergravity with Several Vector Multiplets , Nucl. Phys. B132
1978
Earlier work this paper cites.
M. Gunaydin, G. Sierra and P. K. Townsend, The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras , Nucl. Phys. B242
1984
Earlier work this paper cites.
M. de Roo, Matter Coupling in N=4 Supergravity , Nucl. Phys. B255
1985
Earlier work this paper cites.
E. Bergshoeff, I. G. Koh and E. Sezgin, Coupling of Yang-Mills to N=4, D=4 Supergravity , Phys. Lett. B155
1985
Earlier work this paper cites.
H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings , Nucl.Phys. B269
1986
Earlier work this paper cites.
M. Gunaydin, G. Sierra and P. K. Townsend, More on d = 5 d=5 Maxwell-einstein Supergravity: Symmetric Spaces and Kinks , Class. Quant. Grav. 3
1986
Earlier work this paper cites.
F. A. Berends and W. Giele, The Six Gluon Process as an Example of Weyl-Van Der Waerden Spinor Calculus , Nucl.Phys. B294
1987
Earlier work this paper cites.
M. L. Mangano, S. J. Parke and Z. Xu, Duality and Multi - Gluon Scattering , Nucl. Phys. B298
1988
Earlier work this paper cites.
M. L. Mangano, The Color Structure of Gluon Emission , Nucl.Phys. B309
1988
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders , Nucl.Phys. B312
1989
Earlier work this paper cites.
J. H. Schwarz, Dilaton - axion symmetry , in International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions Rome, Italy, September 21-26, 1992 , pp. 503–520, 1992, hep-th/9209125
1992
Earlier work this paper cites.
Z. Bern, D. C. Dunbar and T. Shimada, String based methods in perturbative gravity , Phys. Lett. B312
1993
Earlier work this paper cites.
M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory . Addison-Wesley, 1995
1995
Earlier work this paper cites.
Z. Bern, L. J. Dixon, M. Perelstein and J. Rozowsky, Multileg one loop gravity amplitudes from gauge theory , Nucl.Phys. B546
1999
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl.Phys. B715
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys.Rev.Lett. 94
2005
Earlier work this paper cites.
S. D. Badger, E. W. N. Glover, V. V. Khoze and P. Svrcek, Recursion relations for gauge theory amplitudes with massive particles , JHEP 07
2005
Earlier work this paper cites.
S. Badger, E. N. Glover and V. V. Khoze, Recursion relations for gauge theory amplitudes with massive vector bosons and fermions , JHEP 0601
2006
Earlier work this paper cites.
Yu. M. Zinoviev, Massive supermultiplets with spin 3/2 , JHEP 05
2007
Earlier work this paper cites.
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string . Cambridge University Press, 2007
2007
Earlier work this paper cites.
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys.Rev. D78
Original
2008
Earlier work this paper cites.
N. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes , Phys.Rev.Lett. 103
Original
2009
Earlier work this paper cites.

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2019

Double copy for massive quantum particles with spin

Johansson, Henrik, Ochirov, Alexander

Understand

The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations.

Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy.
In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves.
Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples.

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.
I. L. Buchbinder, M. V. Khabarov, T. V. Snegirev and Yu. M. Zinoviev, Lagrangian formulation of the massive higher spin N=1 supermultiplets in A d S 4 AdS_{4} space , Nucl. Phys. B942
Original
1901
Earlier work this paper cites.
Y. F. Bautista and A. Guevara, From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems , 1903.12419
Original
1903
Earlier work this paper cites.
W. Cho and K. Lee, Heterotic Kerr-Schild Double Field Theory and Classical Double Copy , JHEP 07
Original
1904
Earlier work this paper cites.
M. Carrillo Gonzalez, B. Melcher, K. Ratliff, S. Watson and C. D. White, The classical double copy in three spacetime dimensions , 1904.11001
Original
1904
Earlier work this paper cites.
A. Brandhuber and G. Travaglini, On higher-derivative effects on the gravitational potential and particle bending , 1905.05657
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, On Post-Minkowskian Hamiltonians in General Relativity , 1906.01579
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes , 1906.09260
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes , 1906.10071
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y.-t. Huang and D. O’Connell, Kerr Black Holes as Elementary Particles , 1906.10100
Original
1906
Earlier work this paper cites.
J. Plefka, C. Shi, J. Steinhoff and T. Wang, Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO , 1906.05875
Original
1906
Earlier work this paper cites.
M. M. Anber, Self-conjugate QCD , 1906.10315
Original
1906
Earlier work this paper cites.
A. Ochirov and B. Page, Multi-Quark Colour Decompositions from Unitarity , 1908.02695
Original
1908
Earlier work this paper cites.
Z. Bern, C. Boucher-Veronneau and H. Johansson, N ≥ \geq 4 Supergravity Amplitudes from Gauge Theory at One Loop , Phys.Rev. D84
Original
1935
Earlier work this paper cites.
F. J. Belinfante, On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields , Physica 7
1940
Earlier work this paper cites.
L. Rosenfeld, Sur le tenseur D’Impulsion-Energie , Acad. Roy. Belg. Memoirs de Classes de Science 18
1940
Earlier work this paper cites.
L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case , Phys. Rev. D9
1974
Earlier work this paper cites.
L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 2. The fermion case , Phys. Rev. D9
1974
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields , vol. 2 of Course of Theoretical Physics . Pergamon Press, Oxford, 1975
1975
Earlier work this paper cites.
J. F. Luciani, Coupling of O(2) Supergravity with Several Vector Multiplets , Nucl. Phys. B132
1978
Earlier work this paper cites.
M. Gunaydin, G. Sierra and P. K. Townsend, The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras , Nucl. Phys. B242
1984
Earlier work this paper cites.
M. de Roo, Matter Coupling in N=4 Supergravity , Nucl. Phys. B255
1985
Earlier work this paper cites.
E. Bergshoeff, I. G. Koh and E. Sezgin, Coupling of Yang-Mills to N=4, D=4 Supergravity , Phys. Lett. B155
1985
Earlier work this paper cites.
H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings , Nucl.Phys. B269
1986
Earlier work this paper cites.
M. Gunaydin, G. Sierra and P. K. Townsend, More on d = 5 d=5 Maxwell-einstein Supergravity: Symmetric Spaces and Kinks , Class. Quant. Grav. 3
1986
Earlier work this paper cites.
F. A. Berends and W. Giele, The Six Gluon Process as an Example of Weyl-Van Der Waerden Spinor Calculus , Nucl.Phys. B294
1987
Earlier work this paper cites.
M. L. Mangano, S. J. Parke and Z. Xu, Duality and Multi - Gluon Scattering , Nucl. Phys. B298
1988
Earlier work this paper cites.
M. L. Mangano, The Color Structure of Gluon Emission , Nucl.Phys. B309
1988
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders , Nucl.Phys. B312
1989
Earlier work this paper cites.
J. H. Schwarz, Dilaton - axion symmetry , in International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions Rome, Italy, September 21-26, 1992 , pp. 503–520, 1992, hep-th/9209125
1992
Earlier work this paper cites.
Z. Bern, D. C. Dunbar and T. Shimada, String based methods in perturbative gravity , Phys. Lett. B312
1993
Earlier work this paper cites.
M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory . Addison-Wesley, 1995
1995
Earlier work this paper cites.
Z. Bern, L. J. Dixon, M. Perelstein and J. Rozowsky, Multileg one loop gravity amplitudes from gauge theory , Nucl.Phys. B546
1999
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl.Phys. B715
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys.Rev.Lett. 94
2005
Earlier work this paper cites.
S. D. Badger, E. W. N. Glover, V. V. Khoze and P. Svrcek, Recursion relations for gauge theory amplitudes with massive particles , JHEP 07
2005
Earlier work this paper cites.
S. Badger, E. N. Glover and V. V. Khoze, Recursion relations for gauge theory amplitudes with massive vector bosons and fermions , JHEP 0601
2006
Earlier work this paper cites.
Yu. M. Zinoviev, Massive supermultiplets with spin 3/2 , JHEP 05
2007
Earlier work this paper cites.
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string . Cambridge University Press, 2007
2007
Earlier work this paper cites.
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys.Rev. D78
Original
2008
Earlier work this paper cites.
N. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes , Phys.Rev.Lett. 103
Original
2009
Earlier work this paper cites.