References on Asymptotic Expansions

C. M. Bender and S. A. Orszag, ``Advanced Mathematical Methods for Scientists and Engineers'', McGraw-Hill Book Company, New York, 1978, pp. 218ff.

J. Matthews and R. L. Walker, ``Mathematical Methods of Physics (second edition)'', Addison-Wesley, Redwood City CA, 1970, p. 80.

References on Quantum Electrodynamics

Toichiro Kinoshita, one of my colleagues here at Cornell, is leading the effort in doing careful high-order calculations in quantum electrodynamics. I've drawn my information from two papers of his: The Fine Structure Constant, Rep. Prog. Phys. 59, pp. 1459 (1996), and ``Massively Parallel Computation and the Anomalous Magnetic Moment of the Electron'', to be published.

The latest measurements of g-2 were done by B. Odom, D. Hanneke, B. D'Urso, and G. Gabrielse, Phys. Rev. Lett. 97, 030801 (2006). The latest theoretical calculation is G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, Phys. Rev. Lett. 97, 030802 (2006). A review of the history of this measurement can be found in A. Rich and J. C. Wesley, Reviews of Modern Physics 44 pp. 250 (1972), and in T. Kinoshita, Shelter Island II edited by R. Jackiw, N. N. Khuri, S. Weinberg, and E. Witten (Cambridge, MA: MIT Press) pp. 278-97 (1985).

The quantum Hall measurements of were done by A. Jeffrey et al., 1996 Conference on Precision Electromagnetic Measurements (17-20 June, 1996, Braunschweig, Germany).

The AC Josephson measurements of were done by E. R. Williams et al., 1989 IEEE Trans. Instrum. Meas. 38, pp. 233.

The neutron mass measurements of were done by E. Krueger, W. Nistler, and W. Weirauch, 1995 Metrologia 32 p. 117.

Freeman J. Dyson, Physical Review 85, 631 (1952), proved that quantum electrodynamics is an asymptotic expansion in the fine structure constant ; that is, the power series does not converge even for as small as 1/137.


Last modified: May 24, 1997

James P. Sethna,

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).