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Anomalous Magnetic Moment of the Electron and the Lamb Shift

Prerequisites Chaps. 16, 23 and 26

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Abstract

Two celebrated experiments involving the observation of the electron anomalous magnetic momentand of the Lamb shift have stimulated much of the development of quantum field theory in the early days.

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Notes

  1. 1.

    Kush and Foley [8].

  2. 2.

    See Lamb and Retherford [9] for the early experiment.

  3. 3.

    A careful derivation of the Lamb shift was particularly carried out by Erickson and Yennie [3]; Fox and Yennie [5]. A highly sophisticated and a very careful derivation, spelling out the finest details, is also given by Julian Schwinger [14].

  4. 4.

    Gordon [6].

  5. 5.

    Schwinger [13]. For a text-book treatment when the electron is also just treated non-relativistically, see Manoukian [10], p. 453, with the corrective factor given by \([1+\kappa (\alpha /2\pi )]\), where \(\kappa =(16/9)-2\,\text {ln}(3/2)\simeq 0.97\), which compares well with the QED result.

  6. 6.

    Feynman [4], p. 7.

  7. 7.

    See, e.g.., Kinoshita [7].

  8. 8.

    C. N. Yang [15], p. 176, writes that Enrico Fermi, Edward Teller, Gregor Wentzel, together with several graduate students including himself gathered into Fermi’s office from April to May in 1948, after attending lectures given, in particular, by Schwinger and Feynman at the New York APS meeting in January 1948, to try to understand, with much difficulty, some of Schwinger’s computations in QED such as the anomaly. At the end of the six weeks of work, somebody asked, “Wasn’t it true that Feynman also talked. All three said,“Yes, yes, Feynman did talk”, “What did he say? ”. All they could remember from Feynman’s lecture, however, was the strange notation of a p with a slash in it: , as a notation standing for \(\gamma p\). Surprisingly, Fermi was taking notes while attending Schwinger’s talk which apparently was unusual for Fermi to take notes in a lecture.

  9. 9.

    A derivation of this expression used often in classical electrodynamics is derived for the convenience of the reader in Box 51.2.

  10. 10.

    For the very elaborate and explicit construction of the four component-wave-functions \(\psi _{n=2,\ell }\), for the problem at hand, see: Manoukian [11], pp. 295–298. See also Manoukian [10], pp. 383, 384, 407.

  11. 11.

    The integral in (27.30) may, of course, be rigorously defined with a cut-off and, as seen above, does not contribute in computing differences in energy levels.

  12. 12.

    See, in particular, Bethe, Brown and Stehn [2]; Schwartz and Tiemann [12].

  13. 13.

    MHz stands for megahertz, 1 MHz equivalent to \(\simeq 4.1357 \times 10^{-9}\,\text {eV}\).

  14. 14.

    See, e.g.., Kinoshita and Yennie [7].

  15. 15.

    For a treatment and a pedagogical presentation of the Lamb shift when the electron is treated all along non-relativistically see Manoukian [10]. The calculation is in the spirit of the first calculation of the Lamb shift carried out by Bethe [1].

References

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  2. Bethe, H. A., Brown, L. M., & Stehn, J. R. (1950). Numerical value of the Lamb shift. Physical Review, 77, 370–374.

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  3. Erickson, G. W., & Yennie, D. R. (1965). Radiative level shifts. I. Formulation and lowest order Lamb shift. Annals of Physics (NY), 35, 271–313.

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  4. Feynman, R. (1990). QED: The strange theory of light and matter. Westminster: Penguin.

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  5. Fox, J. A., & Yennie, D. R. (1973). Some formal aspects of the Lamb shift problem. Annals of Physics (NY), 81, 438–480.

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  7. Kinoshita, T. & Yennie, D. R. (1990). High precision tests of quantum electrodynamics - an overview. In Kinoshita, T. (Ed.) (1990). Quantum electrodynamics: Advanced series on directions in high energy physics (Vol. 7). Singapore: World Scientific.

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  8. Kush, P., & Foley, H. M. (1948). The magnetic moment of the electron. Physical Review, 74, 250–263.

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  1. The Institute for Fundamental Study, Naresuan University, Phitsanulok, Thailand

    E. B. Manoukian

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Manoukian, E.B. (2020). Anomalous Magnetic Moment of the Electron and the Lamb Shift. In: 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand. Springer, Cham. https://doi.org/10.1007/978-3-030-51081-7_27

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