QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga
by Silvan Schweber, Princeton, pp 732, £65/ $99.50 hbk, £29.95/
Theoretical physicists seem a pretty manic-depressive bunch. The turn
of the century was a low point, as their classical world fell apart round
their ears. The crisis eased with the unfolding of quantum mechanics in
the early 1920s, and by 1929 such was the physicists’ confidence and elation
that one of the main players in quantum theory, Paul Dirac, was able to
write that all that remained to be done was ‘fitting of the theory with
This turned out to be no small task. Combining quantum mechanics – the
newly developed framework for describing the world of the atom – with Einstein’s
revised notions of space and time as expressed in his ‘relativity ideas’
is related to understanding the interaction of light with matter. Dirac’s
1927 paper on this interaction is seen as the first step tow-ards a theory
now called quantum electro-dynamics or QED, the theory of the electromagnetic
interaction of charged particles.
In the 1930s, quantum theory grew to become quantum field theory, in
which both electrons and electromagnetic particles, or photons, are represented
as infinite sums over waves. All this, and the experimental confirmation
of antimatter as predicted by Dirac, should have made the 1930s a great
time. But as the decade progressed doubts grew about the structure of quantum
field theory and its usefulness as the basis of a theory of quantum electrodynamics.
Depression set in again.
The problem that caused so much anguish seems on the face of it almost
a technicality. Physicists realised that all but the simplest calculations
using the fledgling quantum field theory and, in particular, its application
to interacting charged particles, gave infinite answers. Everywhere there
were divergences – equations that behaved like fractions with zeros in the
denominator. Technical or not, it was enough to render the whole setup virtually
In the five years following the Second World War, four giants of 20th-century
physics fixed the divergence problem. In doing so, they saved the whole
edifice of quantum field theory, and gave the world a working quantum electrodynamics.
Julian Schwinger and Sinitiro Tomonaga devised a way of working round the
divergences using a prescription based on redefining particle mass and electric
charge, a process called ‘renormalisation’. Richard Feynman devised a parallel
scheme, and in particular a powerful calculational system using diagrams
that was destined to bring field theory calculations to the masses. Freeman
Dyson showed that Feynman’s scheme was equivalent to that of Schwinger and
Tomonaga, and proved that quantum electrodynamics was fully amenable to
the renormalisation prescription. Glory days.
To underscore the significance of their contribution, a quantum field
theory of any other fundamental force these days lives or dies depending
on whether it submits to renormalisation. Both strong and weak electromagnetic
forces are understood using renormalisable quantum field theories based
on QED as a prototype.
Silvan Schweber’s QED and the Men Who Made It details the history of
quantum electrodynamics from the earliest efforts to weld together quantum
theory and relativity right up to the form of the theory as it stands today.
A significant chunk of the book covers the early work of Dirac and others.
But the emphasis is on the late 1940s and, as the title suggests, on the
lives and contributions of the four main players, each of whom merits a
chapter to himself.
Schweber is professor of physics and Richard Koret Professor of the
History of Ideas at Brandeis University in Massachusetts, and in this work
he has probed deep. There is serious discussion of physics interspersed
with insightful biographical material, text of original letters between
great names of the day, and first-hand accounts from past students. The
challenges, influences, key papers and conferences are all beautifully explained,
and Schweber backs up his account with 65 pages of notes and 51 pages of
This is an absorbing, balanced and beautifully written book. Words like
‘outstanding’ and ‘masterpiece’ spring to mind. Superlatives aside, it is
fair to say that Schweber’s book belongs on the shelves devoted to the
history of science, rather than in the popular science section. His style
tends to the erudite rather than popularist; the equations are real ones,
and quite plentiful, but it’s the magic words and those equations that give
the game away. So you happen to know already what renormalisation and wave
functions are then you are well ahead. In short, this book is aimed at an
audience that knows some quantum mechanics and mathematics.
Anybody who does is going to enjoy it and will value the insights it
offers into the technical and human struggle behind one of the greatest
achievement in physics. I am not sure quite what defines a classic work,
but whatever it is I am certain Schweber’s book has it.
Andrew Watson is in the mathematics department of the University of