Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron

Robert Karplus; Norman M. Kroll

doi:10.1103/PhysRev.77.536

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Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron

Robert Karplus^* and Norman M. Kroll^†,‡

Institute for Advanced Study, Princeton, New Jersey

^*Frank B. Jewett Fellow.
^†National Research Council Fellow.
^‡Now at Columbia University, New York, New York.

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Phys. Rev. 77, 536 – Published 15 February, 1950

DOI: https://doi.org/10.1103/PhysRev.77.536

Abstract

The covariant $S$ matrix formalism of Dyson has been applied to the calculation of the fourth-order radiative correction to the magnetic moment of the electron. Intermediate results for the covariant $Δ$ -functions which describe the interaction of virtual electrons and photons with the vacuum are given to order $α$ . The addition to the magnetic moment to order $α^{2}$ is found to be finite after the charge of the electron is renormalized consistently. This correction amounts to $\frac{- 2.97 α^{2}}{π^{2}}$ Bohr magneton so that the magnetic moment of the electron is $μ = 1.001147$ Bohr magnetons.

References (25)

F. J. Dyson, Phys. Rev. 75, 486, 1736 1949
P. Kush and H. M. Foley, Phys. Rev. 74, 250 (1948)
[1], II, Eqs. (6) and (7)
[1], I, Section V
[1], II, Section II
[1]
J. Steinberger, Phys. Rev. 76, 1180 (1949)
Wendell H. Furry, Phys. Rev. 51, 125 (1937)
Omitted endnote
F. J. Dyson, "Longitudinal Photons in Quantum Electrodynamics," Phys. Rev. (to be published)
Julian Schwinger, Phys. Rev. 76, 790 (1949)
Omitted endnote
Omitted endnote
Omitted endnote
R. P. Feynman, Phys. Rev. 76, 769 (1949)
Omitted endnote
F. Bloch and A. Nordsieck, Phys. Rev. 52, 54 (1937)
[1], II
[1], II
Julian Schwinger, Phys. Rev. 76, 790 (1949)
Omitted endnote
Julian Schwinger, Phys. Rev. 73, 415 (1948)
Omitted endnote
Omitted endnote
H. F. Sandham, J. Lon. Math. Soc. 24, 83 (1949)

[c1] F. J. Dyson, Phys. Rev. 75, 486, 1736 1949

[c2] P. Kush and H. M. Foley, Phys. Rev. 74, 250 (1948)

[c3] [1], II, Eqs. (6) and (7)

[c4] [1], I, Section V

[c5] [1], II, Section II

[c6] [1]

[c7] J. Steinberger, Phys. Rev. 76, 1180 (1949)

[c8] Wendell H. Furry, Phys. Rev. 51, 125 (1937)

[c9] Omitted endnote

[c10] F. J. Dyson, "Longitudinal Photons in Quantum Electrodynamics," Phys. Rev. (to be published)

[c11] Julian Schwinger, Phys. Rev. 76, 790 (1949)

[c12] Omitted endnote

[c13] Omitted endnote

[c14] Omitted endnote

[c15] R. P. Feynman, Phys. Rev. 76, 769 (1949)

[c16] Omitted endnote

[c17] F. Bloch and A. Nordsieck, Phys. Rev. 52, 54 (1937)

[c18] [1], II

[c19] [1], II

[c20] Julian Schwinger, Phys. Rev. 76, 790 (1949)

[c21] Omitted endnote

[c22] Julian Schwinger, Phys. Rev. 73, 415 (1948)

[c23] Omitted endnote

[c24] Omitted endnote

[c25] H. F. Sandham, J. Lon. Math. Soc. 24, 83 (1949)

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Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron

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References (25)

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