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Vacuum polarisation tensors in constant electromagnetic fields. I. (English) Zbl 0971.81182
Summary: For Part II see ibid. 585, 429-442 (2000). The string-inspired technique is used for the calculation of vacuum polarisation tensors in constant electromagnetic fields. In the first part of this series, we give a detailed exposition of the method for the case of the QED one-loop \(N\)-photon amplitude in a general constant electromagnetic background field. The two-point cases are calculated explicitly, leading to compact representations for the constant field vacuum polarisation tensors for both scalar and spinor QED.

MSC:
81V10 Electromagnetic interaction; quantum electrodynamics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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References:
[1] Euler, H.; Kockel, B., Naturwissenschaften, Vol. 23, 246, (1935)
[2] Heisenberg, W.; Euler, H., Z. phys., Vol. 98, 714, (1936)
[3] Weisskopf, V.; Dan, K., (), Vidensk. selsk. mat. fy. medd., Vol. 14, 1, (1936), reprint
[4] Ritus, V.I., The Lagrangian function of an intense electromagnetic field and quantum electrodynamics at short distances, () · Zbl 1097.81675
[5] Dittrich, W.; Reuter, M., Effective Lagrangians in quantum electrodynamics, (1985), Springer
[6] Greiner, W.; Reinhardt, J., Quantum electrodynamics, (1992), Springer
[7] Dittrich, W.; Gies, H., Vacuum birefringence in strong magnetic fields, (), 29
[8] Pengo, R., Vacuum birefringence in strong magnetic fields, (), 59
[9] Fock, V., Physik. Z. sowjetunion, Vol. 12, 404, (1937)
[10] Schwinger, J., Phys. rev., Vol. 82, 664, (1951)
[11] Toll, J., Phd thesis, (1952), Princeton University, unpublished
[12] Minguzzi, A., Nuovo cimento, Nuovo cimento, Nuovo cimento, Vol. 19, 847, (1961)
[13] Baier, R.; Breitenlohner, P., Acta phys. austr., Nuovo cimento, Vol. 47, 261, (1967)
[14] Constantinescu, D.H., Nucl. phys. B, Vol. 36, 121, (1972)
[15] Tsai, W.-Y.; Erber, T., Phys. rev. D, Vol. 10, 492, (1974)
[16] Cover, R.A.; Kalman, G., Phys. rev. lett., Vol. 33, 1113, (1974)
[17] Shabad, A.E., Ann. phys., Vol. 90, 166, (1975)
[18] Narozhnyi, N.B., Sov. phys. JETP, Vol. 28, 371, (1969)
[19] Ritus, V.I., Ann. phys., Vol. 69, 555, (1972)
[20] Batalin, I.A.; Shabad, A.E., Sov. phys. JETP, Vol. 33, 483, (1971)
[21] Baier, V.N.; Katkov, V.M.; Strakhovenko, V.M., Sov. phys. JETP, Sov. phys. JETP, Vol. 41, 190, (1975)
[22] Urrutia, L.F., Phys. rev. D, Vol. 71, 1977, (1978)
[23] Artimovich, G.K., Sov. phys. JETP, Vol. 70, 787, (1990)
[24] Gies, H., Phd thesis, (1999), Tübingen University
[25] Bialynicka-Birula, Z.; Bialynicka-Birula, I., Phys. rev. D, Vol. 2, 2341, (1970)
[26] Adler, S.L., Ann. phys. (N.Y.), Vol. 67, 599, (1971)
[27] Raffelt, G.G., Stars as laboratories for fundamental physics, (1996), University of Chicago Press Chicago
[28] Baring, M.G.; Harding, A.K.
[29] V.M. Kaspi et al., to appear in the Proc. of Stellar Endpoints, AGN and the Diffuse Background, Bologna, 1999
[30] Bakalov, D., unpublished
[31] Lee, S.A., Measurement of the magnetically-induced QED birefringence of the vacuum and an improved laboratory search for light pseudoscalars, FERMILAB-PROPOSAL-P-877A, (1998)
[32] Géhéniau, J., Physica, Vol. 16, 822, (1950)
[33] Tsai, W.Y., Phys. rev. D, Vol. 10, 1342, (1974)
[34] Bern, Z.; Kosower, D.A., Phys. rev. D, Phys. rev. lett., Nucl. phys. B, Vol. 379, 451, (1992)
[35] Bern, Z.; Dixon, L.; Kosower, D.A., Phys. rev. lett., Vol. 70, 2677, (1993)
[36] Bern, Z.; Dunbar, D.C.; Shimada, T., Phys. lett. B, Vol. 312, 277, (1993)
[37] Dunbar, D.C.; Norridge, P.S., Nucl. phys. B, Vol. 433, 181, (1995)
[38] Bern, Z.; Dunbar, D.C., Nucl. phys. B, Vol. 379, 562, (1992)
[39] Strassler, M.J., Nucl. phys. B, Vol. 385, 145, (1992)
[40] Schmidt, M.G.; Schubert, C., Phys. rev. D, Vol. 53, 2150, (1996)
[41] Schmidt, M.G.; Schubert, C., Phys. lett. B, Vol. 318, 438, (1993)
[42] Cangemi, D.; D’Hoker, E.; Dunne, G., Phys. rev. D, Vol. 51, 2513, (1995)
[43] Gusynin, V.P.; Shovkovy, I.A., Can. J. phys., Vol. 74, 282, (1996)
[44] Shaisultanov, R., Phys. lett. B, Vol. 378, 354, (1996)
[45] Reuter, M.; Schmidt, M.G.; Schubert, C., Ann. phys., Vol. 259, 313, (1997)
[46] Adler, S.L.; Schubert, C., Phys. rev. lett., Vol. 77, 1695, (1996)
[47] Shovkovy, I.A., Phys. lett. B, Vol. 441, 313, (1998)
[48] Fliegner, D.; Schmidt, M.G.; Schubert, C., Z. phys. C, Vol. 64, 111, (1994)
[49] Fliegner, D.; Haberl, P.; Schmidt, M.G.; Schubert, C., Ann. phys. (N.Y.), Vol. 264, 51, (1998)
[50] Schmidt, M.G.; Schubert, C., Phys. lett. B, Vol. 331, 69, (1994)
[51] Daikouji, K.; Shino, M.; Sumino, Y., Phys. rev. D, Vol. 53, 4598, (1996)
[52] Roland, K.; Sato, H.-T., Nucl. phys. B, Vol. 480, 99, (1996)
[53] Fliegner, D.; Reuter, M.; Schmidt, M.G.; Schubert, C., Theor. math. phys., Vol. 113, 1442, (1997)
[54] Körs, B.; Schmidt, M.G., Eur. phys. J. C, Vol. 6, 175, (1999)
[55] Dunne, G.V.; Schubert, C., Nucl. phys. B, Vol. 564, 591, (2000)
[56] Bern, Z., (), 471
[57] Schubert, C., Lectures given at 36th Cracow school of theoretical physics, Zakopane, 1996, Acta phys. polon. B, Vol. 27, 3965, (1996)
[58] Fried, H.M., Functional methods and models in quantum field theory, (1972), MIT Press Cambridge
[59] Barducci, A.; Bordi, F.; Casalbuoni, R., Nuovo cimento B, Vol. 64, 287, (1981)
[60] Batalin, I.A.; Fradkin, E.S.; Shvartsman, Sh.M., Nucl. phys. B, Vol. 258, 435, (1985)
[61] Rajeev, S.G., Ann. phys., Vol. 173, 249, (1987)
[62] Fradkin, E.S.; Gitman, D.M.; Shvartsman, S.M., Quantum electrodynamics with unstable vacuum, (1991), Springer
[63] McKeon, D.G.C.; Sherry, T.N., Mod. phys. lett. A, Vol. 9, 2167, (1994)
[64] Feynman, R.P., Phys. rev., Vol. 80, 440, (1950)
[65] Green, M.B.; Schwarz, J.H.; Witten, E., Superstring theory, (1987), Cambridge Univ. Press
[66] Itzykson, C.; Zuber, J., Quantum field theory, (1985), McGraw-Hill
[67] Fradkin, E.S., Nucl. phys., Vol. 76, 588, (1966)
[68] Casalbuoni, R., Nuovo cimento A, Vol. 33, 389, (1976)
[69] Berezin, F.A.; Marinov, M.S., Ann. phys., Vol. 104, 336, (1977)
[70] Schubert, C., Eur. phys. J. C, Vol. 5, 693, (1998)
[71] Schubert, C., to appear in the Proc. of Corfu Summer Institute on Elementary Particle Physics, 1998
[72] Weinberg, S., The quantum theory of fields, Vol. 1, (1995), Cambridge Univ. Press
[73] Morgan, A., Phys. lett. B, Vol. 351, 249, (1995)
[74] Schubert, C., Nucl. phys. B, Vol. 585, 429, (2000), next article in this issue
[75] McKeon, D.G.C.; Schubert, C., Phys. lett. B, Vol. 440, 101, (1998)
[76] Dilkes, F.A.; McKeon, D.G.C.; Schubert, C., J. high energy phys., Vol. 03, 022, (1999)
[77] McKeon, D.G.C.; Rebhan, A., Phys. rev. D, Vol. 48, 2891, (1993)
[78] A.I. Karanikas, C.N. Ktorides, JHEP 9911, 033, hep-th/9905027
[79] Haack, M.; Schmidt, M.G., Eur. phys. J. C, Vol. 7, 149, (1999)
[80] Sato, H.-T.
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