Graviton scattering amplitudes in first quantisation

Authors

  • James Edwards Universidad Michoacana de San Nicolás de Hidalgo

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.020729

Keywords:

Quantum Field Theory, Gravitons, Scattering Amplitudes, Worldline Formalism

Abstract

We give a pedagogical review to alternative, first quantised approaches to calculating graviton scattering amplitudes, giving an introduction to string inspired approaches and presenting more recent work based on the worldline formalism of quantum field theory that is motivated by these historic results. We describe how these first quantised techniques can greatly simplify the determination of such amplitudes, in particular reducing the number of Feynman-like diagrams that enter the computation and leading to compact results.

References

J. Schwinger, On Quantum-Electrodynamics and the Magnetic Moment of the Electron, Phys. Rev. 73 (1948) 416, https://doi.org/10.1103/PhysRev.73.416.

A. Petermann, Fourth order magnetic moment of the electron Helv. Phys. Acta 30 (1957) 407, https://doi.org/10.5169/seals-112823.

C. Sommerfield, Magnetic Dipole Moment of the Electron, Phys. Rev. 107 (1957) 328.

S. Laporta and E. Remiddi, The Analytical value of the electron (g-2) at order α 3 in QED, Phys. Lett. B 379 (1996) 283, https://doi.org/10.1016/0370-2693(96)00439-X.

S. Laporta, High-precision calculation of the 4-loop contribution to the electron g-2 in QED, Phys. Lett. B 772 (2017) 232, https://doi.org/10.1016/j.physletb.2017.06.056.

T. Aoyama, T. Kinoshita and M. Nio, Revised and improved value of the QED tenth-order electron anomalous magnetic moment, Phys. Rev. D 97 (2018) 036001, https://doi.org/10.1103/PhysRevD.97.036001.

S. Volkov, Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops, Phys. Rev. D 100 (2019) 096004 https://doi.org/10.1103/PhysRevD.100.096004.

P. Cvitanovic, Asymptotic Estimates and Gauge Invariance, Nucl. Phys. B 127 (1977) 176 https://doi.org/10.1016/0550-3213(77)90357-1.

Z. Bern, D. C. Dunbar and T. Shimada, String-Based Methods in Perturbative Gravity, Phys. Lett. B 312 (1993) 277, https://doi.org/10.1016/0370-2693(93)91081-W.

Z. Bern and D. A. Kosower, Color decomposition of one-loop amplitudes in gauge theories, Nucl. Phys. B 362 (1991) 389, https://doi.org/10.1016/0550-3213(91)90567-H.

Z. Bern and D. A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379(1992) 451, https://doi.org/10.1016/0550-3213(92)90134-W.

M. J. Strassler, Field theory without Feynman diagrams: One loop effective actions, Nucl. Phys. B 385 (1992) 145, https://doi.org/10.1016/0550-3213(92)90098-V.

R. P. Feynman, Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction, Phys. Rev. 80 (1950) 440, https://doi.org/10.1103/PhysRev.80.440.

R.P. Feynman, An Operator Calculus Having Applications in Quantum Electrodynamics, Phys. Rev. 84 (1951) 108, https://doi.org/10.1103/PhysRev.84.108.

H. Kawai, D. C. Lewellen and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B269 (1986) 1-23, https://doi.org/10.1016/0550-3213(86)90362-7.

Z. Bern, Perturbative quantum gravity and its relation to gauge theory, Living Rev. Rel. 5 (2002) 5, https://doi.org/10.12942/lrr-2002-5.

R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499, https://doi.org/10.1016/j.nuclphysb.2005.02.030.

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) 181602, https://doi.org/10.1103/PhysRevLett.94.181602.

Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217, https://doi.org/10.1016/0550-3213(94)90179-1.

F. Cachazo, S. He and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001, https://doi.org/10.1103/PhysRevD.90.065001.

Z. Bern, J. J. M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011, https://doi.org/10.1103/PhysRevD.78.085011.

J. Scherk, Zero-slope limit of the dual resonance model, Nucl. Phys. B 31 (1971) 222, https://doi.org/10.1016/0550-3213(71)90227-6.

T. Yoneya, Quantum gravity and the zero slope limit of the generalized Virasoro model, Lett. Nuovo Cim. 8 (1973) 951, https://doi.org/10.1007/BF02727806.

J. Scherk and J. H. Schwarz, Dual Models for Nonhadrons, Nucl. Phys. B 81 (1974) 118, https://doi.org/10.1016/0550-3213(74)90010-8.

C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept. 355 (2001) 73, https://doi.org/10.1016/S0370-1573(01)00013-8.

P. Mansfield, String theory, Rept. Prog. Phys. 53 (1990) 1183, https://doi.org/10.1088/0034-4885/53/9/002.

J. P. Edwards and C. Schubert, Quantum mechanical path integrals in the first quantised approach to quantum field theory, [arXiv:1912.10004 [hep-th]].

O. Corradini, C. Schubert, J. P. Edwards and N. Ahmadiniaz, Spinning Particles in Quantum Mechanics and Quantum Field Theory, [arXiv:1512.08694 [hep-th]].

J. P. Edwards, C. M. Mata, U. Müller and C. Schubert, New Techniques for Worldline Integration, SIGMA 17 (2021) 065, https://doi.org/10.3842/SIGMA.2021.065.

F.A. Berends, W.T. Giele and H. Kuijf, On relations between multi-gluon and multi-graviton scattering, Phys. Lett. B211 (1988) 91, https://doi.org/10.1016/0370-2693(88)90813-1.

M. B. Green, J. H. Schwarz and L. Brink, N=4 Yang-Mills and N=8 Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474, https://doi.org/10.1016/0550-3213(82)90336-4.

D. C. Dunbar and P. S. Norridge, Calculation of graviton scattering amplitudes using string based methods, Nucl. Phys. B 433 (1995) 181, https://doi.org/10.1016/0550-3213(94)00385-R.

N. Ahmadiniaz, F. M. Balli, O. Corradini, C. LopezArcos, A. Q. Velez and C. Schubert, Manifest colourkinematics duality and double-copy in the string-based formalism, [arXiv:2110.04853 [hep-th]].

H. Elvang and Y. t. Huang, Scattering Amplitudes, [arXiv:1308.1697 [hep-th]].

F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background, Nucl. Phys. B 642 (2002) 372, https://doi.org/10.1016/S0550-3213(02)00683-1.

F. Bastianelli and R. Bonezzi, One-loop quantum gravity from a worldline viewpoint, JHEP 07 (2013) 016, https://doi.org/10.1007/JHEP07(2013)016.

Downloads

Published

2022-08-16

How to Cite

1.
Edwards J. Graviton scattering amplitudes in first quantisation . Supl. Rev. Mex. Fis. [Internet]. 2022 Aug. 16 [cited 2022 Oct. 4];3(2):020729 1-9. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6160