Abstract
Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles.
In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The “angle dependent” large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg’s soft photon theorem.
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References
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [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].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
A. Ashtekar, Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J. Math. Phys. 22 (1981) 2885 [INSPIRE].
A. Ashtekar and M. Streubel, Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity, Proc. Roy. Soc. Lond. A 376 (1981) 585 [INSPIRE].
A. Ashtekar, Quantization of the Radiative Modes of the Gravitational Field, in Quantum Gravity 2, C.J. Isham, R. Penrose and D.W. Sciama (eds.), Oxford University Press, Oxford U.K. (1981).
A. Ashtekar, Asymptotic Quantization, Bibliopolis, Naples Italy (1987).
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.
A. Mohd, A note on asymptotic symmetries and soft-photon theorem, JHEP 02 (2015) 060 [arXiv:1412.5365] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028.
M. Campiglia and A. Laddha, New symmetries for the Gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
J. Fröhlich, G. Morchio and F. Strocchi, Infrared problem and spontaneous breaking of the Lorentz group in QED, Phys. Lett. B 89 (1979) 61 [INSPIRE].
A.P. Balachandran, S. Vaidya, Spontaneous Lorentz Violation in Gauge Theories, Eur. Phys. J. Plus 128 (2013) 118.
A.P. Balachandran, S. Kurkcuoglu, A.R. de Queiroz and S. Vaidya, Spontaneous Lorentz Violation: The Case of Infrared QED, Eur. Phys. J. C 75 (2015) 89 [arXiv:1406.5845] [INSPIRE].
S. Pasterski, Asymptotic Symmetries and Electromagnetic Memory, arXiv:1505.00716 [INSPIRE].
A. Ashtekar and J.D. Romano, Spatial infinity as a boundary of space-time, Class. Quant. Grav. 9 (1992) 1069 [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, arXiv:1506.02906 [INSPIRE].
V.P. Frolov, Null Surface Quantization and Quantum Field Theory in Asymptotically Flat Space-Time, Fortsch. Phys. 26 (1978) 455 [INSPIRE].
C. Dappiaggi, V. Moretti and N. Pinamonti, Rigorous steps towards holography in asymptotically flat spacetimes, Rev. Math. Phys. 18 (2006) 349 [gr-qc/0506069] [INSPIRE].
A. Ashtekar, L. Bombelli and O. Reula, The covariant phase space of asymptotically flat gravitational fields, in Analysis, Geometry and Mechanics: 200 Years After Lagrange, ed. M Francaviglia, North-Holland (1991).
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [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].
A. Ashtekar and K.S. Narain, Infrared problems and Penrose’s null infinity, Syracuse University preprint (1981).
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ArXiv ePrint: 1505.05346
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Campiglia, M., Laddha, A. Asymptotic symmetries of QED and Weinberg’s soft photon theorem. J. High Energ. Phys. 2015, 115 (2015). https://doi.org/10.1007/JHEP07(2015)115
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DOI: https://doi.org/10.1007/JHEP07(2015)115