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One-particle reducible contribution to the one-loop scalar propagator in a constant field. (English) Zbl 1373.81402
Summary: Recently, Gies and Karbstein showed that the two-loop Euler-Heisenberg Lagrangian receives a finite one-particle reducible contribution in addition to the well-known one-particle irreducible one. Here, we demonstrate that a similar contribution exists for the propagator in a constant field already at the one-loop level, and we calculate this contribution for the scalar QED case. We also present an independent derivation of the Gies-Karbstein result using the worldline formalism, treating the scalar and spinor QED cases in a unified manner.

81V10 Electromagnetic interaction; quantum electrodynamics
78A25 Electromagnetic theory, general
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[1] Heisenberg, W.; Euler, H., Folgerungen aus der diracschen theorie des positrons, Z. Phys., 98, 714, (1936) · Zbl 0013.18503
[2] Dittrich, W.; Gies, H., Probing the quantum vacuum, Springer Tracts in Modern Physics, vol. 166, (2000), Springer-Verlag Berlin
[3] Itzykson, C.; Zuber, J., Quantum field theory, (1985), McGraw-Hill
[4] Dávila, J. M.; Schubert, C.; Trejo, M. A., Photonic processes in Born-Infeld theory, Int. J. Mod. Phys. A, 29, (2014) · Zbl 1306.81310
[5] Rebhan, A.; Turk, G., Polarization effects in light-by-light scattering: Euler-Heisenberg versus Born-Infeld · Zbl 1364.81245
[6] Ellis, J.; Mavromatos, N.; You, T., Light-by-light scattering constraint on Born-Infeld theory
[7] Toll, J. S., The dispersion relation for light and its application to problems involving electron pairs, (1952), Princeton University Press, PhD thesis
[8] Adler, S. L., Photon splitting and photon dispersion in a strong magnetic field, Ann. Phys., 67, 599, (1971)
[9] Bialynicka-Birula, Z.; Bialynicka-Birula, I., Nonlinear effects in quantum electrodynamics. photon propagation and photon splitting in an external field, Phys. Rev. D, 2, 2341, (1970)
[10] Baier, V. N.; Milshtein, A. I.; Shaisultanov, R., Photon splitting in a very strong magnetic field, Phys. Rev. Lett., 77, 1691, (1996)
[11] Adler, S. L.; Schubert, C., Photon splitting in a strong magnetic field: recalculation and comparison with previous calculations, Phys. Rev. Lett., 77, 1695, (1996)
[12] Martin, L. C.; Schubert, C.; Villanueva Sandoval, V. M., On the low-energy limit of the QED N-photon amplitudes, Nucl. Phys. B, 668, 335, (2003) · Zbl 1031.81675
[13] Schwinger, J., On gauge invariance and vacuum polarization, Phys. Rev., 82, 664, (1951) · Zbl 0043.42201
[14] Dunne, G. V., (Shifman, M. A.; etal., From Fields to Strings: Circumnavigating Theoretical Physics. Ian Kogan Memorial Collection, (2004)), 445
[15] Weisskopf, V., Über die elektrodynamik des vakuums auf grund der quantentheorie des elektrons, (Schwinger, J., Quantum Electrodynamics, (1958), Dover New York), XIV, 6, (1936), reprinted · Zbl 0016.23806
[16] Ritus, V. I., Lagrangian of an intense electromagnetic field and quantum electrodynamics at short distances, Zh. Eksp. Teor. Fiz., Sov. Phys. JETP, 42, 774, (1975)
[17] Ritus, V. I., Connection between strong-field quantum electrodynamics with short-distance quantum electrodynamics, Zh. Eksp. Teor. Fiz., Sov. Phys. JETP, 46, 423, (1977)
[18] Ritus, V. I., The Lagrangian function of an intense electromagnetic field, (Ginzburg, V. I., Issues in Intense-Field Quantum Electrodynamics, Proc. Lebedev Phys. Inst., vol. 168, (1987), Nova Science Pub. NY)
[19] Fock, V., Die eigenzeit in der klassischen und in der quantenmechanik, Phys. Z. Sowjetunion, 12, 404, (1937) · Zbl 0018.18303
[20] Dittrich, W.; Reuter, M., Effective Lagrangians in quantum electrodynamics, (1985), Springer
[21] Reuter, M.; Schmidt, M. G.; Schubert, C., Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals, Ann. Phys., 259, 313, (1997) · Zbl 0988.81523
[22] Fliegner, D.; Reuter, M.; Schmidt, M. G.; Schubert, C., The two-loop Euler-Heisenberg Lagrangian in dimensional renormalization, Teor. Mat. Fiz., Theor. Math. Phys., 113, 1442, (1997)
[23] Körs, B.; Schmidt, M. G., The effective two loop Euler-Heisenberg action for scalar and spinor QED in a general constant background field, Eur. Phys. J. C, 6, 175, (1999)
[24] Huet, I.; McKeon, D. G.C.; Schubert, C., Euler-Heisenberg Lagrangians and asymptotic analysis in \(1 + 1\) QED. part I: two-loop, J. High Energy Phys., 1012, (2010) · Zbl 1294.81301
[25] Huet, I.; Rausch de Traubenberg, M.; Schubert, C.; Asorey, M.; Bordag, M.; Elizalde, E., The Euler-Heisenberg Lagrangian beyond one loop, Proc. of Eleventh Conference on Quantum Field Theory Under the Influence of External Conditions, QFEXT ’11, Int. J. Mod. Phys. Conf. Ser., 14, 1, 383, (2012)
[26] Huet, Idrish; de Traubenberg, Michel Rausch; Schubert, Christian, Asymptotic behavior of the QED perturbation series · Zbl 1404.81298
[27] Gies, H.; Karbstein, F., An addendum to the Heisenberg-Euler effective action beyond one loop, J. High Energy Phys., 1703, (2017) · Zbl 1377.83032
[28] Strassler, M. J., Field theory without Feynman diagrams: one-loop effective actions, Nucl. Phys. B, 385, 145, (1992)
[29] Schmidt, M. G.; Schubert, C., On the calculation of effective actions by string methods, Phys. Lett. B, 318, 438, (1993)
[30] Schmidt, M. G.; Schubert, C., Multiloop calculations in the string-inspired formalism: the single spinor-loop in QED, Phys. Rev. D, 53, 2150, (1996)
[31] Shaisultanov, R. Zh., On the string-inspired approach to QED in external field, Phys. Lett. B, 378, 354, (1996)
[32] Schubert, C., Vacuum polarisation tensors in constant electromagnetic fields: part I, Nucl. Phys. B, 585, 407, (2000) · Zbl 0971.81182
[33] Schubert, C., Perturbative quantum field theory in the string-inspired formalism, Phys. Rep., 355, 73, (2001) · Zbl 0988.81108
[34] Dunne, G. V.; Schubert, C., Two-loop Euler-Heisenberg QED pair-production rate, Nucl. Phys. B, 564, 59, (2000)
[35] Dunne, G. V.; Huet, A.; Rivera, D.; Schubert, C., Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians, J. High Energy Phys., 0611, (2006)
[36] Bern, Z.; Kosower, D. A., Efficient calculation of one loop QCD amplitudes, Phys. Rev. Lett., 66, 1669, (1991)
[37] Bern, Z.; Kosower, D. A., The computation of loop amplitudes in gauge theory, Nucl. Phys. B, 379, 451, (1992)
[38] Ahmad, A.; Ahmadiniaz, N.; Corradini, O.; Kim, S. P.; Schubert, C., Master formulas for the dressed scalar propagator in a constant field, Nucl. Phys. B, 919, 9, (2017) · Zbl 1361.81163
[39] Bastianelli, F.; van Nieuwenhuizen, P., Path integrals and anomalies in curved space, (2006), Cambridge University press · Zbl 1120.81057
[40] Fradkin, E. S.; Gitman, D. M.; Shvartsman, S. M., Quantum electrodynamics with unstable vacuum, (1991), Springer
[41] Kuznetsov, A.; Mikheev, N., Electroweak processes in external electromagnetic fields, Springer Tracts in Modern Physics, (2004), Springer · Zbl 1058.81734
[42] Ritus, V. I., Method of eigenfunctions and mass operator in quantum electrodynamics of a constant field, Zh. Eksp. Teor. Fiz., Sov. Phys. JETP, 48, 788, (1978)
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