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Reducible contributions to quantum electrodynamics in external fields. (English) Zbl 1416.81209
Summary: We consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one-loop and two-loop order. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one loop and beyond. Our calculations are exact in the external fields and we give strong and weak field expansions in the magnetic case.
81V10 Electromagnetic interaction; quantum electrodynamics
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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[1] W. Heisenberg and H. Euler, Consequences of Diracs theory of positrons, Z. Phys.98 (1936) 714 [physics/0605038] [INSPIRE].
[2] V. Weisskopf, Über die Elektrodynamik des Vakuums auf Grund der Quantentheorie des Elektrons, Kong. Dans. Vid. Selsk. Math-fys. Medd. XIV6 (1936) .
[3] Schwinger, JS, On gauge invariance and vacuum polarization, Phys. Rev., 82, 664, (1951) · Zbl 0043.42201
[4] G.V. Dunne, Heisenberg-Euler effective Lagrangians: Basics and extensions, in From fields to strings: Circumnavigating theoretical physics. Ian Kogan memorial collection (3 volume set), M. Shifman et al. eds., World Scientific, Singapore (2004), hep-th/0406216 [INSPIRE].
[5] G.V. Dunne, New strong-field QED effects at ELI: nonperturbative vacuum pair production, Eur. Phys. J.D 55 (2009) 327 [arXiv:0812.3163] [INSPIRE].
[6] Bell, AR; Kirk, JG, Possibility of prolific pair production with high-power lasers, Phys. Rev. Lett., 101, 200403, (2008)
[7] A.M. Fedotov, N.B. Narozhny, G. Mourou and G. Korn, Limitations on the attainable intensity of high power lasers, Phys. Rev. Lett.105 (2010) 080402 [arXiv:1004.5398] [INSPIRE].
[8] S.S. Bulanov et al., Multiple colliding electromagnetic pulses: a way to lower the threshold of e+\(e\)−pair production from vacuum, Phys. Rev. Lett.104 (2010) 220404 [arXiv:1003.2623] [INSPIRE].
[9] A. Gonoskov et al., Probing nonperturbative QED with optimally focused laser pulses, Phys. Rev. Lett.111 (2013) 060404 [arXiv:1302.4653] [INSPIRE].
[10] CILEX, http://cilexsaclay.fr/.
[11] CoReLS, http://corels.ibs.re.kr/.
[12] ELI, https://eli-laser.eu/.
[13] European XFEL, https://www.xfel.eu/.
[14] G.V. Dunne and C. Schubert, Two-loop Euler-Heisenberg QED pair-production rate, Nucl. Phys.B 564 (2000) 591.
[15] I. Huet, M. Rausch De Traubenberg and C. Schubert, Three-loop Euler-Heisenberg Lagrangian in 1 + 1 QED, part 1: single fermion-loop part, JHEP03 (2019) 167 [arXiv:1812.08380] [INSPIRE]. · Zbl 1414.81262
[16] G.V. Dunne and C. Schubert, Closed form two loop Euler-Heisenberg Lagrangian in a selfdual background, Phys. Lett.B 526 (2002) 55 [hep-th/0111134] [INSPIRE].
[17] G.V. Dunne and C. Schubert, Two loop selfdual Euler-Heisenberg Lagrangians. 1. Real part and helicity amplitudes, JHEP08 (2002) 053 [hep-th/0205004] [INSPIRE]. · Zbl 1226.81294
[18] G.V. Dunne and C. Schubert, Two loop selfdual Euler-Heisenberg Lagrangians. 2. Imaginary part and Borel analysis, JHEP06 (2002) 042 [hep-th/0205005] [INSPIRE].
[19] Schneider, C.; Schützhold, R., Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields, JHEP, 02, 164, (2016)
[20] G. Torgrimsson, C. Schneider, J. Oertel and R. Schützhold, Dynamically assisted Sauter-Schwinger effectNon-perturbative versus perturbative aspects, JHEP06 (2017) 043 [arXiv:1703.09203] [INSPIRE].
[21] G. Torgrimsson, C. Schneider and R. Schützhold, Sauter-Schwinger pair creation dynamically assisted by a plane wave, Phys. Rev.D 97 (2018) 096004 [arXiv:1712.08613] [INSPIRE].
[22] F. Karbstein and E.A. Mosman, Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams, Phys. Rev.D 96 (2017) 116004 [arXiv:1711.06151] [INSPIRE].
[23] N. Ahmadiniaz, A. Huet, A. Raya and C. Schubert, Full mass range analysis of the QED effective action for an O(2) × \(O\)(3) symmetric field, Phys. Rev.D 87 (2013) 125020 [arXiv:1305.1606] [INSPIRE].
[24] L.C. Martin, C. Schubert and V.M. Villanueva Sandoval, On the low-energy limit of the QED N photon amplitudes, Nucl. Phys.B 668 (2003) 335 [hep-th/0301022] [INSPIRE].
[25] J.P. Edwards, A. Huet and C. Schubert, On the low-energy limit of the QED N-photon amplitudes: part 2, Nucl. Phys.B 935 (2018) 198 [arXiv:1807.10697] [INSPIRE]. · Zbl 1398.81279
[26] B. King and T. Heinzl, Measuring vacuum polarisation with high power lasers, arXiv:1510.08456 [INSPIRE].
[27] V.I. Ritus, Quantum effects of the interaction of elementary particles with an intense electromagnetic field, J. Russ. Laser Res.6 (1985) 497.
[28] Piazza, A.; Muller, C.; Hatsagortsyan, KZ; Keitel, CH, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys., 84, 1177, (2012)
[29] D. Seipt, Volkov states and non-linear Compton scattering in short and intense laser pulses, in the proceedings of Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks (HQ 2016), July 18-30, Dubna, Russia (2017), arXiv:1701.03692.
[30] Gies, H.; Karbstein, F., An addendum to the Heisenberg-Euler effective action beyond one loop, JHEP, 03, 108, (2017) · Zbl 1377.83032
[31] F. Karbstein, Heisenberg-Euler effective action in slowly varying electric field inhomogeneities of Lorentzian shape, Phys. Rev.D 95 (2017) 076015 [arXiv:1703.08017] [INSPIRE].
[32] Karbstein, F., Tadpole diagrams in constant electromagnetic fields, JHEP, 10, 075, (2017) · Zbl 1383.81352
[33] W. Dittrich and H. Gies, Probing the quantum vacuum. Perturbative effective action approach in quantum electrodynamics and its application, Springer Tracts Mod. Phys.166 (2000) 1.
[34] Dittrich, W.; Reuter, M., Effective Lagrangians in quantum electrodynamics, Lect. Notes Phys., 220, 1, (1985)
[35] J.P. Edwards and C. Schubert, One-particle reducible contribution to the one-loop scalar propagator in a constant field, Nucl. Phys.B 923 (2017) 339 [arXiv:1704.00482] [INSPIRE]. · Zbl 1373.81402
[36] N. Ahmadiniaz et al., One-particle reducible contribution to the one-loop spinor propagator in a constant field, Nucl. Phys.B 924 (2017) 377 [arXiv:1704.05040] [INSPIRE].
[37] D.G.C. McKeon and T.N. Sherry, Radiative effects in a constant magnetic field using the quantum mechanical path integral, Mod. Phys. Lett.A 9 (1994) 2167 [INSPIRE].
[38] A. Ahmad et al., Master formulas for the dressed scalar propagator in a constant field, Nucl. Phys.B 919 (2017) 9 [arXiv:1612.02944] [INSPIRE].
[39] N. Ahmadiniaz, A. Bashir and C. Schubert, Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED, Phys. Rev.D 93 (2016) 045023 [arXiv:1511.05087] [INSPIRE].
[40] V.A. Fock, Proper time in classical and quantum field theory, Sow. Phys.12 (937) 404.
[41] J. Schwinger, Particles, sources, and fields. Volume 1, Addison Wesley, U.S.A. (1970).
[42] T. Heinzl et al., On the observation of vacuum birefringence, Opt. Commun.267 (2006) 318 [hep-ph/0601076] [INSPIRE].
[43] I.K. Affleck, O. Alvarez and N.S. Manton, Pair production at strong coupling in weak external fields, Nucl. Phys.B 197 (1982) 509 [INSPIRE].
[44] Ritus, VI, Method of eigenfunctions and mass operator in quantum electrodynamics of a constant field, Sov. Phys. JETP, 48, 788, (1978)
[45] M. Formanek et al., Strong fields and neutral particle magnetic moment dynamics, Comments Plasma Phys. Contr. Fusion60 (2018) 074006 [arXiv:1712.07698] [INSPIRE].
[46] S. Meuren and A. Di Piazza, Quantum electron self-interaction in a strong laser field, Phys. Rev. Lett.107 (2011) 260401 [arXiv:1107.4531] [INSPIRE].
[47] A. Ilderton and G. Torgrimsson, Radiation reaction from QED: lightfront perturbation theory in a plane wave background, Phys. Rev.D 88 (2013) 025021 [arXiv:1304.6842] [INSPIRE].
[48] J.M. Cole et al., Experimental evidence of radiation reaction in the collision of a high-intensity laser pulse with a laser-wakefield accelerated electron beam, Phys. Rev.X 8 (2018) 011020 [arXiv:1707.06821] [INSPIRE].
[49] K. Poder et al., Experimental signatures of the quantum nature of radiation reaction in the field of an ultraintense laser, Phys. Rev.X 8 (2018) 031004 [arXiv:1709.01861] [INSPIRE].
[50] M.J. Strassler, Field theory without Feynman diagrams: one loop effective actions, Nucl. Phys.B 385 (1992) 145 [hep-ph/9205205] [INSPIRE].
[51] C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept.355 (2001) 73 [hep-th/0101036] [INSPIRE].
[52] M.G. Schmidt and C. Schubert, On the calculation of effective actions by string methods, Phys. Lett.B 318 (1993) 438 [hep-th/9309055] [INSPIRE].
[53] J.P. Edwards and C. Schubert, Quantum mechanical path integrals in the first quantised approach to quantum field theory, technical report (2018).
[54] Schwinger, J., On gauge invariance and vacuum polarization, Phys. Rev., 82, 664, (1951) · Zbl 0043.42201
[55] M. Reuter, M.G. Schmidt and C. Schubert, Constant external fields in gauge theory and the spin 0\(,\) 1\(/\)2\(,\) 1 path integrals, Annals Phys.259 (1997) 313 [hep-th/9610191] [INSPIRE].
[56] W. Dittrich and R. Shaisultanov, Vacuum polarization in QED with worldline methods, Phys. Rev.D 62 (2000) 045024 [hep-th/0001171] [INSPIRE].
[57] R. Shaisultanov, On the string inspired approach to QED in external field, Phys. Lett.B 378 (1996) 354 [hep-th/9512142] [INSPIRE].
[58] N. Ahmadiniaz et al., Worldline master formulas for the dressed electron propagator, parts 1 and 2, in preparation.
[59] Hostler, LC, Scalar formalism for quantum electrodynamics, J. Math. Phys., 26, 1348, (1985)
[60] A.G. Morgan, Second order fermions in gauge theories, Phys. Lett.B 351 (1995) 249 [hep-ph/9502230] [INSPIRE].
[61] V.I. Ritus, The Lagrange function of an intensive electromagnetic field and quantum electrodynamics at small distances, Sov. Phys. JETP42 (1975) 774 [Pisma Zh. Eksp. Teor. Fiz69 (1975) 1517].
[62] F. Karbstein, An all-loop result for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian, arXiv:1903.06998 [INSPIRE].
[63] G.V. Dunne, Heisenberg-Euler effective Lagrangians: basics and extensions, in From fields to strings: circumnavigating theoretical physics. Ian Kogan memorial collection (3 volume set), M. Shifman et al., World Scientific, Singapore (2004), hep-th/0406216 [INSPIRE].
[64] G.V. Dunne, H. Gies and C. Schubert, Zero modes, β-functions and IR/UV interplay in higher loop QED, JHEP11 (2002) 032 [hep-th/0210240] [INSPIRE].
[65] A. Ilderton and G. Torgrimsson, Worldline approach to helicity flip in plane waves, Phys. Rev.D 93 (2016) 085006 [arXiv:1601.05021] [INSPIRE]. · Zbl 1364.81243
[66] V. Dinu, T. Heinzl and A. Ilderton, Infra-red divergences in plane wave backgrounds, Phys. Rev.D 86 (2012) 085037 [arXiv:1206.3957] [INSPIRE].
[67] A. Casher, Gauge fields on the null plane, Phys. Rev.D 14 (1976) 452 [INSPIRE].
[68] S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept.301 (1998) 299 [hep-ph/9705477] [INSPIRE].
[69] Feynman, RP, An operator calculus having applications in quantum electrodynamics, Phys. Rev., 84, 108, (1951) · Zbl 0044.23304
[70] G.V. Dunne and C. Schubert, Worldline instantons and pair production in inhomogeneous fields, Phys. Rev.D 72 (2005) 105004 [hep-th/0507174] [INSPIRE].
[71] Ilderton, A., Localisation in worldline pair production and lightfront zero-modes, JHEP, 09, 166, (2014) · Zbl 1333.81282
[72] M.B. Halpern and P. Senjanovic, Functional bridge between gauge theory and string in two-dimensions, Phys. Rev.D 15 (1977) 1655 [INSPIRE].
[73] M.B. Halpern, A. Jevicki and P. Senjanovic, Field theories in terms of particle-string variables: spin, internal symmetries and arbitrary dimension, Phys. Rev.D 16 (1977) 2476 [INSPIRE].
[74] T.W.B. Kibble, A. Salam and J.A. Strathdee, Intensity dependent mass shift and symmetry breaking, Nucl. Phys.B 96 (1975) 255 [INSPIRE].
[75] C. Harvey, T. Heinzl, A. Ilderton and M. Marklund, Intensity-dependent electron mass shift in a laser field: existence, universality and detection, Phys. Rev. Lett.109 (2012) 100402 [arXiv:1203.6077] [INSPIRE].
[76] A. Ilderton and G. Torgrimsson, Radiation reaction in strong field QED, Phys. Lett.B 725 (2013) 481 [arXiv:1301.6499] [INSPIRE]. · Zbl 1364.81243
[77] L.S. Brown and T.W.B. Kibble, Interaction of intense laser beams with electrons, Phys. Rev.133 (1964) A705 [INSPIRE].
[78] E. Lundstrom et al., Using high-power lasers for detection of elastic photon-photon scattering, Phys. Rev. Lett.96 (2006) 083602 [hep-ph/0510076] [INSPIRE].
[79] H. Gies, F. Karbstein and C. Kohlfürst, All-optical signatures of strong-field QED in the vacuum emission picture, Phys. Rev.D 97 (2018) 036022 [arXiv:1712.03232] [INSPIRE].
[80] E.S. Fradkin, D.M. Gitman and S.M. Shvartsman, Quantum electrodynamics with unstable vacuum, Springer, Germany (1991).
[81] R.P. Mignani et al., Evidence for vacuum birefringence from the first optical-polarimetry measurement of the isolated neutron star RX J1856.5-3754, Mon. Not. Roy. Astron. Soc.465 (2017) 492 [arXiv:1610.08323] [INSPIRE].
[82] L.M. Capparelli, A. Damiano, L. Maiani and A.D. Polosa, A note on polarized light from Magnetars, Eur. Phys. J.C 77 (2017) 754 [arXiv:1705.01540] [INSPIRE].
[83] R. Turolla et al., A comment onA note on polarized light from Magnetars: QED effects and axion-like particlesby L.M. Capparelli, L. Maiani and A.D. Polosa, arXiv:1706.02505 [INSPIRE].
[84] I. Caiazzo and J. Heyl, Vacuum birefringence and the X-ray polarization from black-hole accretion disks, Phys. Rev.D 97 (2018) 083001 [arXiv:1803.03798] [INSPIRE].
[85] Schutzhold, R.; Gies, H.; Dunne, G., Dynamically assisted Schwinger mechanism, Phys. Rev. Lett., 101, 130404, (2008) · Zbl 1228.81274
[86] A.M. Polyakov, Gauge fields and strings, Contemp. Concepts Phys.3 (1987) 1.
[87] P. Mansfield, String theory, Rept. Prog. Phys.53 (1990) 1183 [INSPIRE].
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