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

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.

- Elastic Theory has Zero Radius of Convergence.
- What is the radius of convergence?
- Famous Asymptotic Series

Last modified: May 24, 1997

James P. Sethna, sethna@lassp.cornell.edu

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