Dashen-Frautschi FiascoOn April 29, at the 1965 spring meeting of the American Physical Society in Washington, Freeman J. Dyson of the Institute of Advanced Study (Princeton) presented an invited talk entitled "Old and New Fashions in Field Theory," and the content of his talk was published in the June issue of the Physic Today, on page 21-24. This paper contains the following paragraph.
The first of these two achievements is the explanation of the mass difference between neutron and proton by Roger Dashen, working at the time as a graduate student under the supervision of Steve Frautschi. The neutron-proton mass difference has for thirty years been believed to be electromagnetic in origin, and it offers a splendid experimental test of any theory which tries to cover the borderline between electromagnetic and strong interactions. However, no convincing theory of the mass-difference had appeared before 1964. In this connection I exclude as unconvincing all theories, like the early theory of Feynman and Speisman, which use one arbitrary cut-off parameter to fit one experimental number. Dashen for the first time made an honest calculation without arbitrary parameters and got the right answer. His method is a beautiful marriage between old-fashioned electrodynamics and modern bootstrap techniques. He writes down the equations expressing the fact that the neutron can be considered to be a bound state of a proton with a negative pi meson, and the proton a bound state of a neutron with a positive pi meson, according to the bootstrap method. Then into these equations he puts electromagnetic perturbations, the interaction of a photon with both nucleon and pi meson, according to the Feynman rules. The calculation of the resulting mass difference is neither long nor hard to understand, and in my opinion, it will become a classic in the history of physics.Dyson was talking about the paper by R. F. Dashen and S. C. Frautschi published in Phys. Rev. 135, B1190 and B1196 (1964). They use the S-matrix formalism for bound states.
Later in the same year, Steve Adler and Roger Dashen became full professors at the Institute for Advanced Study. Naturally, they were admired by their colleagues, and many young physicists studied Dashen's paper on the neutron-proton mass difference. I was one of those who studied the paper carefully during the summer of 1965. I then published a paper in the Physical Review [142, 1150 (1966)].
In their paper, Dashen and Frautschi use the S-matrix method to calculate
a perturbed energy level. Of course, they use approximations because
they are dealing with strong interactions. If we translate what they
did into the language of the Schrödinger picture, they are using the
following approximation for
(φ, δV φ),
There are however "good" and "bad" approximations. I showed in my paper that Dashen and Frautschi use the formula
(φ good , δV φbad) .
I then pointed out their infrared divergence comes from this bad approximation.
Dashen and Frautschi use the S-matrix formalism where the bound-states appear as poles in the complex energy plane. A slight mislocation will lead to the inclusion of the bad wave function. This is precisely the course of the so-called "Dashen-Frautschi Fiasco."
In 1997, I attended his 70th birthday celebration held at MIT. My wife and I posed with him in this photo. We were very happy!
Toward a New Research Program
Feynman was on my side!
|I am standing in front of Feynman's portrait at the entrance of Fermi Lab's Feynman Computing Center (June 2003).|
As for the wave functions, I was particularly interested in their localization property, as you can see from the "good" and "bad" wave functions. The burning issue was and still is whether the hydrogen wave function localized in one Lorentz frame appears to be localized to observers in other Lorentz frames. This is a well-defined problem, and I enjoyed working on this problem in the past. I enjoy giving invited talks on this subject under current titles, such as symmetries of extended particles, covariance of Feynman's parton picture, Feynman's rest of the universe, squeezed states, Feynman's decoherence, Wigner's little groups, and other trademarks of current interest.
You may visit my Scope of Research page to find out what I am talking about.