Abstract
We obtain the subleading tail to the memory term in the late time electromagnetic radiative field generated due to a generic scattering of charged bodies. We show that there exists a new asymptotic conservation law which is related to the subleading tail term. The corresponding charge is made of a mode of the asymptotic electromagnetic field that appears at \( \mathcal{O} \)(e5) and we expect that it is uncorrected at higher orders. This hints that the subleading tail arises from classical limit of a 2-loop soft photon theorem. Building on the m = 1 [41, 42] and m = 2 cases, we propose that there exists a conservation law for every m such that the respective charge involves an \( \mathcal{O} \)(e2m+1) mode and is conserved exactly. This would imply a hierarchy of an infinite number of m-loop soft theorems. We also predict the structure of mth order tails to the memory term that are tied to the classical limit of these soft theorems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Gell-Mann and M.L. Goldberger, Scattering of low-energy photons by particles of spin 1/2, Phys. Rev. 96 (1954) 1433 [INSPIRE].
F.E. Low, Scattering of light of very low frequency by systems of spin 1/2, Phys. Rev. 96 (1954) 1428 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
D.J. Gross and R. Jackiw, Low-Energy Theorem for Graviton Scattering, Phys. Rev. 166 (1968) 1287 [INSPIRE].
C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
R. Ferrari and L.E. Picasso, Spontaneous breakdown in quantum electrodynamics, Nucl. Phys. B 31 (1971) 316 [INSPIRE].
R. Ferrari and L.E. Picasso, Dynamical consequences of spontaneous breakdown of symmetries, Nucl. Phys. B 20 (1970) 553 [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S -matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
M. Campiglia and A. Laddha, New symmetries for the Gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
V. Lysov, S. Pasterski and A. Strominger, Low’s Subleading Soft Theorem as a Symmetry of QED, Phys. Rev. Lett. 113 (2014) 111601 [arXiv:1407.3814] [INSPIRE].
E. Conde and P. Mao, Remarks on asymptotic symmetries and the subleading soft photon theorem, Phys. Rev. D 95 (2017) 021701 [arXiv:1605.09731] [INSPIRE].
M. Campiglia and R. Eyheralde, Asymptotic U(1) charges at spatial infinity, JHEP 11 (2017) 168 [arXiv:1703.07884] [INSPIRE].
Y. Hamada and G. Shiu, Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities, Phys. Rev. Lett. 120 (2018) 201601 [arXiv:1801.05528] [INSPIRE].
Z.-Z. Li, H.-H. Lin and S.-Q. Zhang, Infinite Soft Theorems from Gauge Symmetry, Phys. Rev. D 98 (2018) 045004 [arXiv:1802.03148] [INSPIRE].
H. Elvang, C.R.T. Jones and S.G. Naculich, Soft Photon and Graviton Theorems in Effective Field Theory, Phys. Rev. Lett. 118 (2017) 231601 [arXiv:1611.07534] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic charges in massless QED revisited: A view from Spatial Infinity, JHEP 05 (2019) 207 [arXiv:1810.04619] [INSPIRE].
Z. Bern, S. Davies and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons, Phys. Rev. D 90 (2014) 085015 [arXiv:1405.1015] [INSPIRE].
S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].
B. Sahoo and A. Sen, Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions, JHEP 02 (2019) 086 [arXiv:1808.03288] [INSPIRE].
K.S. Thorne, Gravitational-wave bursts with memory: The Christodoulou effect, Phys. Rev. D 45 (1992) 520 [INSPIRE].
V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts withmemory and experi-mental prospects, Nature 327 (1987) 123.
M. Ludvigsen, Geodesic Deviation At Null Infinity And The Physical Effects Of VeryLong Wave Gravitational Radiation, Gen. Rel. Grav. 21 (1989) 1205 [INSPIRE].
L. Susskind, Electromagnetic Memory, arXiv:1507.02584 [INSPIRE].
L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].
S. Pasterski, Asymptotic Symmetries and Electromagnetic Memory, JHEP 09 (2017) 154 [arXiv:1505.00716] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
A. Laddha and A. Sen, Gravity Waves from Soft Theorem in General Dimensions, JHEP 09 (2018) 105 [arXiv:1801.07719] [INSPIRE].
S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen and M. Verma, Subleading Soft Theorem for Multiple Soft Gravitons, JHEP 12 (2017) 150 [arXiv:1707.06803] [INSPIRE].
A. Laddha and A. Sen, Logarithmic Terms in the Soft Expansion in Four Dimensions, JHEP 10 (2018) 056 [arXiv:1804.09193] [INSPIRE].
A. Laddha and A. Sen, Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem, Phys. Rev. D 100 (2019) 024009 [arXiv:1806.01872] [INSPIRE].
A.P. Saha, B. Sahoo and A. Sen, Proof of the classical soft graviton theorem in D = 4, JHEP 06 (2020) 153 [arXiv:1912.06413] [INSPIRE].
M. Campiglia and A. Laddha, Loop Corrected Soft Photon Theorem as a Ward Identity, JHEP 10 (2019) 287 [arXiv:1903.09133] [INSPIRE].
S. Atul Bhatkar, Ward identity for loop level soft photon theorem for massless QED coupled to gravity, JHEP 10 (2020) 110 [arXiv:1912.10229] [INSPIRE].
V. Namias, Application of the Dirac delta function to electric charge and multipole distributions, Am. J. Phys. 45 (1977) 624.
D.H. Kobe and A.L. Smirl, Gauge Invariant Formulation of the Interaction of Electromagnetic Radiation and Matter, Am. J. Phys. 46 (1978) 624 [INSPIRE].
B. Sahoo, Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions, JHEP 12 (2020) 070 [arXiv:2008.04376] [INSPIRE].
W.D. Goldberger, J. Li and S.G. Prabhu, Spinning particles, axion radiation, and the classical double copy, Phys. Rev. D 97 (2018) 105018 [arXiv:1712.09250] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.03627
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bhatkar, S.A. New asymptotic conservation laws for electromagnetism. J. High Energ. Phys. 2021, 82 (2021). https://doi.org/10.1007/JHEP02(2021)082
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)082