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On this 75th anniversary of the publication of the Heisenberg-Euler paper on the full non-perturbative one-loop effective action for quantum electrodynamics I review their paper and discuss some of the impact it has had on quantum field theory.
E. Whittaker and G. Watson, Modern Analysis
1927
Earlier work this paper cites.
P. A. M. Dirac, “The Quantum theory of electron,” Proc. Roy. Soc. Lond. A117
1928
Earlier work this paper cites.
P. A. M. Dirac, “Quantized Singularities in the Electromagnetic Field,” Proc. Roy. Soc. Lond. A133
1931
Earlier work this paper cites.
F. Sauter, “Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs”, Zeit. f. Phys. 69
1931
Earlier work this paper cites.
P. A. M. Dirac, “Theory of the Positron”, Report to 7th Solvay Conference (1933), Structure and properties of Atomic Nuclei
1934
Earlier work this paper cites.
W. Heisenberg, “The fluctuations of charge connected with the formation of matter from radiation”, Sächsiche Akad. Wissen. 86
1934
Earlier work this paper cites.
W. Heisenberg, “Comments on the Dirac theory of the positron”, Zeit. f. Phys. 90
1934
Earlier work this paper cites.
M. Born, L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. Lond. A144
1934
Earlier work this paper cites.
H. Euler and B. Kockel, “The scattering of light by light in the Dirac theory”, Naturwiss. 23
1935
Earlier work this paper cites.
R. Serber, “Linear modifications in the Maxwell field equations,” Phys. Rev. 48
1935
Earlier work this paper cites.
D. M. Volkov, “Über eine Klasse von Lösungen der Diracschen Gleichung”, Z. Phys. 94
1935
Earlier work this paper cites.
H. Euler, “On the scattering of light by light in Dirac’s theory”, PhD thesis at Univ. Leipzig (1936); published in Ann. Phys. (Leipzig) 26
1936
Earlier work this paper cites.
W. Heisenberg and H. Euler, “Consequences of Dirac’s Theory of Positrons”, Zeit. f. Phys. 98
1936
Earlier work this paper cites.
A. Akhieser, L. Landau and I. Pomeranchuk, “Scattering of light by light”, Nature 138
1937
Earlier work this paper cites.
V. Fock, “Proper Time In Classical And Quantum Mechanics,” Phys. Z. Sow. 12
1937
Earlier work this paper cites.
V. F. Weisskopf, “On the Self-Energy and the Electromagnetic Field of the Electron,” Phys. Rev. 56
1939
Earlier work this paper cites.
E. C. G. Stueckelberg, “La Mecanique du point materiel en theorie de relativite et en theorie des quanta,” Helv. Phys. Acta 15
1942
Earlier work this paper cites.
R. P. Feynman, “The Theory of positrons,” Phys. Rev. 76
1949
Earlier work this paper cites.
R. P. Feynman, “Mathematical formulation of the quantum theory of electromagnetic interaction,” Phys. Rev. 80
1950
Earlier work this paper cites.
Y. Nambu, “The Use Of The Proper Time In Quantum Electrodynamics,” Prog. Theor. Phys. 5
1950
Earlier work this paper cites.
R. P. Feynman, “An Operator calculus having applications in quantum electrodynamics,” Phys. Rev. 84
1951
Earlier work this paper cites.
C. Morette, “On the definition and approximation of Feynman’s path integrals,” Phys. Rev. 81
1951
Earlier work this paper cites.
J. Schwinger, “On gauge invariance and vacuum polarization”, Phys. Rev. 82
1951
Earlier work this paper cites.
R. Karplus and M. Neuman, “The Scattering of Light by Light”, Phys. Rev. 83
1951
Earlier work this paper cites.
J. Schwinger, “The Theory of Quantized Fields. V”, Phys. Rev. 93
1954
Earlier work this paper cites.
B. S. DeWitt, “Quantum Theory of Gravity. 1. The Canonical Theory,” Phys. Rev. 160
1967
Earlier work this paper cites.
E. Brézin and C. Itzykson, “Pair Production In Vacuum By An Alternating Field,” Phys. Rev. D 2
1970
Cited alongside, same era.
Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear Effects in Quantum Electrodynamics. Photon Propagation and Photon Splitting in an External Field”, Phys. Rev. D 10
1970
Cited alongside, same era.
Y. B. Zeldovich, A. A. Starobinsky, “Particle production and vacuum polarization in an anisotropic gravitational field,” Sov. Phys. JETP 34
1972
Cited alongside, same era.
S. R. Coleman and E. Weinberg, “Radiative Corrections As The Origin Of Spontaneous Symmetry Breaking,” Phys. Rev. D 7
1973
Cited alongside, same era.
M. R. Brown and M. J. Duff, “Exact Results For Effective Lagrangians,” Phys. Rev. D 11
1975
Cited alongside, same era.
K. Fujikawa, “A Nondiagramatic Calculation Of One Loop Beta Function In QCD,” Phys. Rev. D 48
1993
Later among the works it cites.
V. Weisskopf, “The electrodynamics of the vacuum based on the quantum theory of the electron”, Kong. Dans. Vid. Selsk. Math-fys. Medd. XIV No. 6 (1936); English translation in: Early Quantum Electrodynamics: A Source Book
1994
Later among the works it cites.
J. Grundberg and T. H. Hansson, “The QCD trace anomaly as a vacuum effect (The vacuum is a medium is the message!),” Ann. Phys. 242
1995
Later among the works it cites.
E. Elizalde, Ten Physical Applications Of Spectral Zeta Functions
1995
Later among the works it cites.
Z. Bern, D. A. Kosower, “The Computation of loop amplitudes in gauge theories,” Nucl. Phys. B379
1996
Later among the works it cites.
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W. -y. Tsai, T. Erber, “Photon Pair Creation in Intense Magnetic Fields,” Phys. Rev. D10
1976
Cited alongside, same era.
J. S. Dowker, R. Critchley, “Effective Lagrangian and Energy Momentum Tensor in de Sitter Space,” Phys. Rev. D13
1976
Cited alongside, same era.
V. S. Popov, “Pair Production in a Variable External Field (Quasiclassical approximation)”, Sov. Phys. JETP 34
1977
Cited alongside, same era.
P. Candelas, D. J. Raine, “General Relativistic Quantum Field Theory-An Exactly Soluble Model,” Phys. Rev. D12
1977
Cited alongside, same era.
M. T. Grisaru and H. N. Pendleton, “Some Properties Of Scattering Amplitudes In Supersymmetric Theories,” Nucl. Phys. B 124
1977
Cited alongside, same era.
S. W. Hawking, “Zeta Function Regularization of Path Integrals in Curved Space-Time,” Commun. Math. Phys. 55
1977
Cited alongside, same era.
H. Pagels and E. Tomboulis, “Vacuum Of The Quantum Yang-Mills Theory And Magnetostatics,” Nucl. Phys. B 143
1978
Cited alongside, same era.
S. L. Adler, J. N. Bahcall, C. G. Callan, M. N. Rosenbluth, “Photon splitting in a strong magnetic field,” Phys. Rev. Lett. 25
1996
Later among the works it cites.
V. P. Gusynin, V. A. Miransky, I. A. Shovkovy, “Dynamical chiral symmetry breaking by a magnetic field in QED,” Phys. Rev. D52
1996
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Sh. Zh. Akhmadaliev et al, “Delbrück scattering at energies of 140-450 MeV”, Phys. Rev. C 58
1998
Later among the works it cites.
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
Later among the works it cites.
S. N. M. Ruijsenaars, “On Barnes’ multiple zeta and gamma functions”, Adv. Math. 156
2000
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C. Schubert, “Perturbative quantum field theory in the string-inspired formalism”, Phys. Rept. 355
2001
Later among the works it cites.
Sh. Zh. Akhmadaliev et al, “ Experimental investigation of high-energy photon splitting in atomic fields”, Phys. Rev. Lett. 89
2002
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K. Kirsten, Spectral Functions in Mathematics and Physics
2002
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A. Ringwald, “Pair production from vacuum at the focus of an X-Ray free electron laser”, Phys. Lett. B 510
2003
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S. M. Kuzenko and I. N. McArthur, “Low-energy dynamics in N = 2 super QED: Two-loop approximation,” JHEP 0310
2004
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L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave”, Sov. Phys. JETP 20
2005
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2008
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G. Farmelo, The Strangest Man: the Life of Paul Dirac
2009
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2009
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R. Schützhold, H. Gies, G. Dunne, “Dynamically assisted Schwinger mechanism,” Phys. Rev. Lett. 101
2009
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2009
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T. Tajima, “Prospect for extreme field science”, Eur. Phys. J. D 55
2009
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H. Gies, “Strong laser fields as a probe for fundamental physics,” Eur. Phys. J. D55
2009
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B. I. Abelev et al
2009
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2010
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Z. Bern, H. Ita, “Harmony of scattering amplitudes: From QCD to gravity,” Nucl. Phys. Proc. Suppl. 216
2011
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