Abstract
The dressed state formalism enables us to define the infrared finite S-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss’s law naturally leads to proper asymptotic states for the infrared finite S-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.
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References
F. Bloch and A. Nordsieck, Note on the radiation field of the electron, Phys. Rev. 52 (1937) 54 [INSPIRE].
D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Annals Phys. 13 (1961) 379 [INSPIRE].
V. Chung, Infrared divergence in quantum electrodynamics, Phys. Rev. 140 (1965) B1110 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. I. Classical currents, J. Math. Phys. 9 (1968) 315 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. II. Mass-shell singularities of Green’s functions, Phys. Rev. 173 (1968) 1527 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. III. Asymptotic states and reduction formulas, Phys. Rev. 174 (1968) 1882 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. IV. The scattering operator, Phys. Rev. 175 (1968) 1624 [INSPIRE].
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [Teor. Mat. Fiz. 4 (1970) 153] [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, JHEP 09 (2018) 121 [arXiv:1803.02370] [INSPIRE].
D. Neuenfeld, Infrared-safe scattering without photon vacuum transitions and time-dependent decoherence, arXiv:1810.11477 [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].
F.J. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75 (1949) 1736 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading, MA, U.S.A. (1995) [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 1: foundations, Cambridge University Press, Cambridge, U.K. (2005) [INSPIRE].
J.D. Dollard, Asymptotic convergence and the Coulomb interaction, J. Math. Phys. 5 (1964) 729.
E. Bagan, M. Lavelle and D. McMullan, Charges from dressed matter: construction, Annals Phys. 282 (2000) 471 [hep-ph/9909257] [INSPIRE].
H. Hirai and S. Sugishita, Conservation laws from asymptotic symmetry and subleading charges in QED, JHEP 07 (2018) 122 [arXiv:1805.05651] [INSPIRE].
Y. Hamada and S. Sugishita, Notes on the gravitational, electromagnetic and axion memory effects, JHEP 07 (2018) 017 [arXiv:1803.00738] [INSPIRE].
M. Fukuma, S. Sugishita and Y. Sakatani, Propagators in de Sitter space, Phys. Rev. D 88 (2013) 024041 [arXiv:1301.7352] [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
S. Mandelstam, Quantum electrodynamics without potentials, Annals Phys. 19 (1962) 1 [INSPIRE].
S. Mandelstam, Feynman rules for electromagnetic and Yang-Mills fields from the gauge independent field theoretic formalism, Phys. Rev. 175 (1968) 1580 [INSPIRE].
I. Heemskerk, Construction of bulk fields with gauge redundancy, JHEP 09 (2012) 106 [arXiv:1201.3666] [INSPIRE].
D. Kabat and G. Lifschytz, CFT representation of interacting bulk gauge fields in AdS, Phys. Rev. D 87 (2013) 086004 [arXiv:1212.3788] [INSPIRE].
D. Harlow, Wormholes, emergent gauge fields and the weak gravity conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
R. Jakob and N.G. Stefanis, Path dependent phase factors and the infrared problem in QED, Annals Phys. 210 (1991) 112 [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, arXiv:1810.05338 [INSPIRE].
H. Hirai and S. Sugishita, work in progress.
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
T.D. Lee and M. Nauenberg, Degenerate systems and mass singularities, Phys. Rev. 133 (1964) B1549 [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. 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].
H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, Asymptotic symmetries in p-form theories, JHEP 05 (2018) 042 [arXiv:1801.07752] [INSPIRE].
M. Campiglia, L. Freidel, F. Hopfmueller and R.M. Soni, Scalar asymptotic charges and dual large gauge transformations, JHEP 04 (2019) 003 [arXiv:1810.04213] [INSPIRE].
D. Francia and C. Heissenberg, Two-form asymptotic symmetries and scalar soft theorems, Phys. Rev. D 98 (2018) 105003 [arXiv:1810.05634] [INSPIRE].
H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, String memory effect, JHEP 02 (2019) 053 [arXiv:1811.07368] [INSPIRE].
M. Henneaux and C. Troessaert, Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity, JHEP 05 (2019) 147 [arXiv:1812.07445] [INSPIRE].
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ArXiv ePrint: 1901.09935
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Hirai, H., Sugishita, S. Dressed states from gauge invariance. J. High Energ. Phys. 2019, 23 (2019). https://doi.org/10.1007/JHEP06(2019)023
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DOI: https://doi.org/10.1007/JHEP06(2019)023