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Modern Physics > Particle Physics > Particles v
Modern Physics > Quantum Physics > Quantum Field Theory > General Quantum Field Theory v



Gyromagnetic Ratio
    

The ratio of the magnetic dipole moment to the mechanical angular momentum of a system.

The electronic spin angular momentum of an electron with spin s is given by

(1)

where is h-bar, and in "classical" quantum mechanics, the corresponding magnetic moment is

(2)

where is the charge on the electron, is the mass of the electron, and c is the speed of light. This gives a value

(3)

where is the Bohr magneton, sometimes known as the Landé factor. The explanation of the factor of 2 appearing in this equation, which should classically be 1 and is caused by orbital electron angular momentum, was one of the successes of Dirac's theory of the electron (Griffiths 1987, p. 153).

Fine Structure Constant




References

Basdevant, J.-L. and Dalibard, J. "Measuring the Electron Magnetic Moment Anomaly." Ch. 11 in The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics. Berlin: Springer-Verlag, pp. 79-81, 2000.

Berestetskii, V. B.; Lifshitz, E. M.; and Ditaevskii, L. P. Quantum Electrodynamics, 2nd ed. Oxford, England: Pergamon Press, pp. 151-158, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, p. 93, 1977.

Cornell Theory Center Press Release. "Digging at the Roots of Physics at the Cornell Theory Center." Sep. 18, 1996. http://www.tc.cornell.edu/er/media/1996/kinoshita.release.html.

Griffiths, D. J. Introduction to Elementary Particles. New York: Wiley, p. 153, 1987.

Hughes, V. W. and Kinoshita, T. "Anomalous g Values of the Electron and Muon." Rev. Mod. Phys. 71, S133-139, 1999.

Karplus, R. and Kroll, N. "Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron." Phys. Rev. 77, 536-549, 1950.

Kinoshita, T. "The Fine Structure Constant." Rept. Prof. Phys. 59, 1459-1492, 1996.

Laporta, S. and Remiddi, E. "The Analytical Value of the Electron at Order in QED." Phys. Lett. B 379, 283-291, 1996. http://xxx.lanl.gov/abs/hep-ph/9602417/

Laporta, S. and Remiddi, E. "Progress in the Analytical Evaluation of the Electron in QED: The Scalar Part of the Triple Cross Graphs." Phys. Lett. B 356, 390-397, 1995.

Sommerfield, C. M. "Magnetic Dipole Moment of the Electron." Phys. Rev. Ser. 2 107, 328-329, 1957.

Van Dyck, R. S. Jr.; Schwinberg, P. B.; and Dehmelt, H. G. "New High Precision Comparison of Electron and Positron g Factors." Phys. Rev. Lett. 59, 26-29, 1987.

Van Dyck, R. S. Jr. "Anomalous Magnetic Moment of Single Electrons and Positrons: Experiment." In Quantum Electrodynamics (Ed. T. Kinoshita). Singapore: World Scientific, pp. 322-388, 1990.







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