Abstract
In this paper we consider introducing careful regularization at the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of Dirac brackets accordingly in a controlled manner. This method is most useful when we consider asymptotic charges that are not localized at the boundary u → ±∞ like large gauge transformations. We show that our method reproduces the operator algebra in known cases, and it can be applied to other space-time symmetry charges such as the BMS transformations. We also obtain the asymptotic form of the U(1) charge following from the electromagnetic duality in an explicitly EM symmetric Schwarz-Sen type action. Using our regularization method, we demonstrate that the charge generates the expected transformation of a helicity operator. Our method promises applications in more generic theories.
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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].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [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, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody symmetry of 4D Yang-Mills theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [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, 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, arXiv:1506.02906 [INSPIRE].
A. Strominger, Magnetic corrections to the soft photon theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12 (2015) 094 [arXiv:1509.01406] [INSPIRE].
T.T. Dumitrescu, T. He, P. Mitra and A. Strominger, Infinite-dimensional fermionic symmetry in supersymmetric gauge theories, arXiv:1511.07429 [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, JHEP 12 (2016) 095 [arXiv:1607.08599] [INSPIRE].
M. Mirbabayi and M. Porrati, Dressed hard states and black hole soft hair, Phys. Rev. Lett. 117 (2016) 211301 [arXiv:1607.03120] [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].
T. He, D. Kapec, A.-M. Raclariu and A. Strominger, Loop-corrected Virasoro symmetry of 4D quantum gravity, JHEP 08 (2017) 050 [arXiv:1701.00496] [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
A. Nande, M. Pate and A. Strominger, Soft factorization in QED from 2D Kac-Moody symmetry, JHEP 02 (2018) 079 [arXiv:1705.00608] [INSPIRE].
R. Bousso and M. Porrati, Soft hair as a soft wig, Class. Quant. Grav. 34 (2017) 204001 [arXiv:1706.00436] [INSPIRE].
A. Ashtekar, Asymptotic quantization: based on 1984 Naples lectures, Humanities Press, (1987) [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].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
E.T. Newman and R. Penrose, Note on the Bondi-Metzner-Sachs group, J. Math. Phys. 7 (1966) 863 [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
G. Barnich and C. Troessaert, Supertranslations call for superrotations, PoS(CNCFG2010)010 [Ann. U. Craiova Phys. 21 (2011) S11] [arXiv:1102.4632] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
S.J. Haco, S.W. Hawking, M.J. Perry and J.L. Bourjaily, The conformal BMS group, JHEP 11 (2017) 012 [arXiv:1701.08110] [INSPIRE].
D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1489 [INSPIRE].
J.H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of chiral (selfdual) P forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
V.P. Frolov, Null surface quantization and quantum field theory in asymptotically flat space-time, Fortsch. Phys. 26 (1978) 455 [INSPIRE].
A. Mohd, A note on asymptotic symmetries and soft-photon theorem, JHEP 02 (2015) 060 [arXiv:1412.5365] [INSPIRE].
S.G. Pasterski, Subtleties of zero modes, unpublished notes, http://physicsgirl.com/zeromodes.pdf.
C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219] [INSPIRE].
C.-S. Chu and P.-M. Ho, Constrained quantization of open string in background B field and noncommutative D-brane, Nucl. Phys. B 568 (2000) 447 [hep-th/9906192] [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University, Princeton U.S.A., (1992) [INSPIRE].
R.M. Wald, General relativity, University of Chicago Press, Chicago U.S.A., (1984) [INSPIRE].
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Bhattacharyya, A., Hung, LY. & Jiang, Y. Null hypersurface quantization, electromagnetic duality and asympotic symmetries of Maxwell theory. J. High Energ. Phys. 2018, 27 (2018). https://doi.org/10.1007/JHEP03(2018)027
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DOI: https://doi.org/10.1007/JHEP03(2018)027