Abstract
We present several results on memory effects, asymptotic symmetry and soft theorems in massive QED. We first clarify in what sense the memory effects are interpreted as the charge conservation of the large gauge transformations, and derive the leading and subleading memory effects in classical electromagnetism. We also show that the sub-subleading charges are not conserved without including contributions from the spacelike infinity. Next, we study QED in the BRST formalism and show that parts of large gauge transformations are physical symmetries by justifying that they are not gauge redundancies. Finally, we obtain the expression of charges associated with the subleading soft photon theorem in massive scalar QED.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
M. Campiglia, L. Coito and S. Mizera, Can scalars have asymptotic symmetries?, Phys. Rev. D 97 (2018) 046002 [arXiv:1703.07885] [INSPIRE].
Y. Hamada and S. Sugishita, Soft pion theorem, asymptotic symmetry and new memory effect, JHEP 11 (2017) 203 [arXiv:1709.05018] [INSPIRE].
M. Campiglia and L. Coito, Asymptotic charges from soft scalars in even dimensions, Phys. Rev. D 97 (2018) 066009 [arXiv:1711.05773] [INSPIRE].
D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Annals Phys. 13 (1961) 379 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [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].
F.E. Low, Scattering of light of very low frequency by systems of spin 1/2, Phys. Rev. 96 (1954) 1428 [INSPIRE].
F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].
T.H. Burnett and N.M. Kroll, Extension of the low soft photon theorem, Phys. Rev. Lett. 20 (1968) 86 [INSPIRE].
M. Gell-Mann and M.L. Goldberger, Scattering of low-energy photons by particles of spin 1/2, Phys. Rev. 96 (1954) 1433 [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].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [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].
Y.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17 [Astron. Zh. 51 (1974) 30].
V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327 (1987) 123.
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
K.S. Thorne, Gravitational-wave bursts with memory: The Christodoulou effect, Phys. Rev. D 45 (1992) 520 [INSPIRE].
L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].
A. Tolish and R.M. Wald, Retarded Fields of Null Particles and the Memory Effect, Phys. Rev. D 89 (2014) 064008 [arXiv:1401.5831] [INSPIRE].
L. Susskind, Electromagnetic Memory, arXiv:1507.02584 [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New Gravitational Memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].
P. Mao and H. Ouyang, Note on soft theorems and memories in even dimensions, Phys. Lett. B 774 (2017) 715 [arXiv:1707.07118] [INSPIRE].
Y. Hamada and S. Sugishita, Notes on the gravitational, electromagnetic and axion memory effects, JHEP 07 (2018) 017 [arXiv:1803.00738] [INSPIRE].
P. Mao, H. Ouyang, J.-B. Wu and X. Wu, New electromagnetic memories and soft photon theorems, Phys. Rev. D 95 (2017) 125011 [arXiv:1703.06588] [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].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
V.P. Frolov, Null Surface Quantization and Quantum Field Theory in Asymptotically Flat Space-Time, Fortsch. Phys. 26 (1978) 455 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of Gauge Theories, Annals Phys. 98 (1976) 287 [INSPIRE].
I.V. Tyutin, Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism, arXiv:0812.0580 [INSPIRE].
Y. Hamada, M.-S. Seo and G. Shiu, Electromagnetic Duality and the Electric Memory Effect, JHEP 02 (2018) 046 [arXiv:1711.09968] [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].
T. Kugo and S. Uehara, General Procedure of Gauge Fixing Based on BRS Invariance Principle, Nucl. Phys. B 197 (1982) 378 [INSPIRE].
T. Kugo and I. Ojima, Manifestly Covariant Canonical Formulation of Yang-Mills Field Theories: Physical State Subsidiary Conditions and Physical S-Matrix Unitarity, Phys. Lett. B 73 (1978) 459 [INSPIRE].
S.N. Gupta, Theory of longitudinal photons in quantum electrodynamics, Proc. Phys. Soc. A 63 (1950) 681 [INSPIRE].
K. Bleuler, A New method of treatment of the longitudinal and scalar photons, Helv. Phys. Acta 23 (1950) 567 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft Hair on Black Holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
C.-S. Chu and Y. Koyama, Soft Hair of Dynamical Black Hole and Hawking Radiation, JHEP 04 (2018) 056 [arXiv:1801.03658] [INSPIRE].
A. Seraj, Multipole charge conservation and implications on electromagnetic radiation, JHEP 06 (2017) 080 [arXiv:1610.02870] [INSPIRE].
G. Compère, R. Oliveri and A. Seraj, Gravitational multipole moments from Noether charges, JHEP 05 (2018) 054 [arXiv:1711.08806] [INSPIRE].
V. Chung, Infrared Divergence in Quantum Electrodynamics, Phys. Rev. 140 (1965) B1110 [INSPIRE].
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [INSPIRE].
J. Ware, R. Saotome and R. Akhoury, Construction of an asymptotic S matrix for perturbative quantum gravity, JHEP 10 (2013) 159 [arXiv:1308.6285] [INSPIRE].
M. Mirbabayi and M. Porrati, Dressed Hard States and Black Hole Soft Hair, Phys. Rev. Lett. 117 (2016) 211301 [arXiv:1607.03120] [INSPIRE].
B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, JHEP 12 (2016) 095 [arXiv:1607.08599] [INSPIRE].
D. Kapec, M. Perry, A.-M. Raclariu and A. Strominger, Infrared Divergences in QED, Revisited, Phys. Rev. D 96 (2017) 085002 [arXiv:1705.04311] [INSPIRE].
S. Choi, U. Kol and R. Akhoury, Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations, JHEP 01 (2018) 142 [arXiv:1708.05717] [INSPIRE].
S. Choi and R. Akhoury, BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes, JHEP 02 (2018) 171 [arXiv:1712.04551] [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G. Semenoff, On the need for soft dressing, arXiv:1803.02370 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1805.05651
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hirai, H., Sugishita, S. Conservation laws from asymptotic symmetry and subleading charges in QED. J. High Energ. Phys. 2018, 122 (2018). https://doi.org/10.1007/JHEP07(2018)122
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2018)122