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1TomonagaS
i
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‑
i
t
i
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o
: A Memorial
TwoShakerso
fP
h
y
s
i
c
s
J
u
l
i
a
nS.Schwinger

Mlnasama:
I am deeply honored to have the privilege of addressing you
today.

It ls natural that I should do so, as the Nobel prize partner

whose work on quantum electrodynamics was most akin in spirit tothatof Tomonaga Sin‑ltlro・ But not until I began preparing this memorial
did I becom
e completely aware of howmuch our scientific lives had
common.

in

I shall mention those aspects in due time. More immediately

provocative ls the curious similarity hidden in our names.τ'he
Japanese character ‑the k.anji
由

those ofto wave ， to shake・shin () has, among other meanings

τ'he beginning of my Germanic name,

Sc
l
.
,
wlng, means ・to swing， to shake・．

Hence my title， Two Shakers ofPhysics・・One cannot speak of Tomonaga without reference to Yukawa Hldeki
and,of course, Nishina Yoshi0 ・ It ls a remarkable coincidence thatboth Japanese Nobel prize winners in physics were horn in Tokyo,
hadtheir families move

to Kyoto,both

and also both were sons ofprofessors at Kyoto University, both attended the Third High School in
Kyoto,

and both attended and graduated from Kyoto Unive‑rslty with

degrees In physics.

In their third and final year at the unlverslty,

both learned the new quantum mechanics together (Tomonaga would later

PAGE 22

remark, about this Independent study, that he was happy not to bebothered by the professors), Both graduated ln 1929 into a world that
seemed to have no place for them, (Yukawa later saldmade scholars ）.

・＇Thedepresslon

Accordingly, both stayed on as unpaid assistants toProfessor Tamaki; Yukawa would eventually succeed him.
Nishina comes on stage.

In 1931,

He gave a series of lectures at Kyoto

Universlty on quantum mechanics.

Sakata Sholchi•

then a student,

later reported that Yukawa and Tomonaga asked the most questions
afterward.
Nishina was a graduate tn electrical engineering of Tokyo
University.

In 1917 he Jolned the recently founded Instltute ofPhysical and Chemical Research, the Rikagaku Kenkyusho ‑ Rik.en.
privateA

institution, Rlken was supported flnaclally ln various ways,

including the holding of patents on the manufacture of sake,Afterseveral years at Rik.en, Nishina was sent abroad for further study, apilgrimage that would last for eight years.

He stopped atCavendish Laboratory in Cambridge, England, atGottingen ln Germany, and then, finally, went。

B hr l且

Copenhagen.

thethe University of

to Denmark and Niels

Ho would staγthere for 冒 1zγear•.

/hat period came the famous Klein‑Nishina formula.

And out of

Nishina returned

to Japan in December, 1928, to begin building the Nishina Group.

Itwould, among other contributions, establish Japan in the forefront ofresearch on nuclear and cosmic ray physics ‑ soryushiron.
There was a branch of Rik.en at Kyoto ln 1931 when Nishina,
embodiment of thethe，・ came to lecture and to bekopenhagener Geist

impressed by Tomonaga.

The acceptance of Nishina g offer of a

research positlon brought Tomonaga to Tokyo in 1932.

（Three years

PAGE 3earlier he had traveled to Tokyo to hear lectures at Rik.en given by
Heisenberg and Dirac.） The year 1932 was a traumatic one for physics.
The neutron was discovered;

the positron was discovered.τ'he

first

collaborative efforts of Nishina and Tomonaga dealt with the neutron,and the problem of nuclear forces.
publications,

Although there were no formal

this work. was reported at

the 1932 autumn and 1933

spring meetings that were regularly held by the Rlken staff.
the1933 autumn m色 eting the subject becomes the positron.

beginning of a Joint research program that would seeofanumberofpaperselectron‑positron pairconcerned

creationandThen, in

It was thethe publication

with various aspects ofannihilation.

Tomonaga scontributions to quantum electrodynamics has begun.
While these papers were visible evidence of interest in quantum
electrodynamics, we areindebted to Tomonaga for telllng us, in his

Nobel address, of an unseen but more important st母 p ‑ he read the 1932
paper of Dirac that attempted to find a new basis for electrodynamics.
Dirac argued thatthe role of the field is to provide a means

making observations of aforsystem of particles， and therefore, "wecannot suppose the field to be a dynamical system on the same footingasthe particles and thus something to be observed in the same way as

the particles ． The attempt to demote the dynamical
elctromagnetlc field,or,in the more extreme

Wheeler and Feynman, to eliminate

itentirely,

status ofthelater proposal of

is a

false

trail,

contrary to the fundamental quantum duality between particle and wave,
or field.

Nevertheless, Dirac g paper was

to be very influential,

Tomonaga says,

・"This paper of Dirac g attracted my interest because of
the novelty of its philosophy and the beauty of its
form. Nishina also showed a great interest in this3

4

PAGE 4

paper and suggested that I investigate the possibilityof predicting some newphenomena by this theory． ThenI started computations to see whether the Kleln‑Nlshlna
formula could be derived from this theory or whether
any modification of the formula might result. I foundout immediately, however, without performlng the
calculation through to the end, that it would yield thesame answer as the previous theory τ'he new theory of
Dirac s was in fact mathematically equivalent to theolder Heisenberg‑Pauli theory and I realized during the
calculation that one could pass form one to the otherby a unitary transformation. The equivalence of these
two theories was also discovered by Rosenfeld andDirac‑Fock‑Podolsky and was soon published in theirpapers."．

I graduated from a high 曹 chool
Harris,that was named for Townsend

the first American con哩ul in .Japan. Soon after, in 1934, I

wrote but did not publish my first research paper.

It was on quantum

eleotrodynamlos.

Several years before, the Danish physicist Moller

had proposed a

relativistic

interaction between twoelectrons,

produced through the retarded intervention of the electromagnetic
field.

It had been known slnc母 1927 that electrons could

described

by acounterpart.

field,

onethat had no classical, macroscopic

And the dynamical

description ofthis fieldunderstood, when the elctrons interacted instantaneously.
things would be when the retarded interaction of
introduced.

also bewas

I asked how
Mollerwas

To answer the question I used the Dirac‑Fock‑Podolsky

formulation. But now, since I was dealing entirely with fields,lt

was natural to introduce for the electron field, as well, the analogueof the unitary transformation that Tomonaga had already recongnized as
being applied tothe electromagnetic fieldin Dirac s

original

version. Here was the first tentative use of what Tomonaga, in 1943,
would

correctly characterize as"a formal transformation which isalmost self‑evident and I, years later, would calltheinteraction

PAGE 5representation.

No,・， had reached what

neither of us, in the 1930

would eventually be named the Tomonaga‑Schwinger equation.

But eachof us held a piece which, in combination, would lead to that equation:
Tornonaga appreciated the relativistic form of
thinking ln particle

language;thetheory,but wasI used a field theory, but had notunderstood the need for a fully relativistic form.

Had we met

then,would history have been different?
The reports of the spring and autumn 1936 meetings of the Rik.en
staff show something new ‑ Tomonaga had resumed his interest in
nuclear physics.

In 1937 he went

to Germany ‑to Heisenberg S

Institute at Leipzig, He would stay for two years, working on nuclear
physics and on the theory of mesons, to use the modern term. Tomonaga
had come with a project in mind:

treat Bohr's liquid drop model ofthe nucleus, and the way an impinging neutron heats it up,

by using

the macroscopic concepts of heat conduction and viscosity.τ'his work.
was published in 1938.
submitted

It was also

the major part ofthethesisto Tokyo University in 1939 for the degree of Doctor of・

Science ‑ Rlgakuhakushi. Heisenberg s interest in oosmlo rays

thenturned Tomonaga s attention to Yukawa， meson.
The not yet understood fact, that the meson of nuclear forcesandthe cosmic ray meson observed at sea level are not the same

particle, was beginning to thoroughly confuse matters at

this

time.

Tomonaga wondered whether the problem of the meson lifetime could beovercome by including an indirect process, in which the meson

turns

into a pair of nucleons ‑ proton and neutron ‑ that annihilate toproduce the final
nucleon pairs,

electron and neutrino・

τ'he integral

over allresulting from the perturbation calculation, was ‑56

PAGE 6

Infinite. Tomonaga kept a diary of his impressions during this German
period.

It poignantly records his emotional

reactionstothedifficulties he encountered. Here are some excerpts:

It has been cold and drizzling since morning and I
have devoted the whole day to physics in vain. As it
got dark I went to the park． I'
he sky was gray with a
bit of the yellow of twilight in it. I could see thesilhouetted white birch grove glowing vaguely in thedark. My view was partly obscured by my tired eyes;
my nose prickled from the cold and upon returning home
I had a nosebleed. After supper I took up my physics
again, but at last I gave up. I11‑starred work
indeed！
τ'hen,
Recently I have felt very sad without any reason, so I
went to a film. Returning home I E・
ead a book on
physics. I don t understand it very well. Meanwhile I
suffer. Why isn t nature clearer and more directly
comprehensible？

・・

Again,As I went on with the calculation, I found theintegral diverged ‑ was infinite. After lunch I went
for a walk. The air was astringently cold and the pondin Johanna Park was half frozen, with ducks swimmingwhere there was no ice. I could see a flock of otherbirds． I'he flower beds were covered with chestnut
leaves against the frost. Walking in the park, I was
no longer interested in the existence of neutron,
neutrino.
And f1na11y,
I complained ln emotional words to Professor Nishina
about the slump in my work, whereupon I got his letterin reply this morning. After reading it my eyes werefilled with tears. ‑ He says: only fortune decides
your progress ln achieve町1ents. Al1 of us stand on thedividing line from which the future ls invisible. We
need not be too anzlous about the results, even though
they may turn out quite different from what you expect.
By‑and‑by you may meet a new chance for success.

・ stay in Leipzig, Heisenberg

Toward the close of Tomonaga s

PAGE 7suggested a possible physical answer to the clear lnappllcablllty of
perturbation methods in meson physics.
of

It involved the self‑reaction

the strong meson field surrounding a nucleon, Heisenberg did aclassical calculation,
nucleons mightshowing thatthe scattering of mesons by

thereby be strongly reduced, which would be more inconformity with the experimental results. About
later

this

idea Tomonaga． Heisenberg, ln this paper publlshed in 1939,

remarkedemphasized that the field reaction would be crucial
scattering.

in meson‑nucleon

Just at that time I was studying at Leipzig, and I still

remember vividly how Heisenberg enthusiastically explained this
to

idea

me and handed me galley proofs of his forthcoming paper.

Influenced by Heisenberg, I came to believe that the problem offield

reactions far from being meaninglesl!I was one which required a frontal
attack. Indeed, Tomonaga wanted to stay on for another year, to workonthequantummechanical， classicalversion of Heisenberg

calculation.
The growing clouds of war made this inadvisable, however,andTomonaga returned to Japan by ship. As it happened, Yukawa who had
come to Europe to attend a Solvay Congress, which unfortunately wascancelled,

sailed on that very ship. When the ship docked at New

York., Yuk.awa disembarked and, beginning at Columbia University,

where

I first met him, made his way across the United States, visiting
various universities.
York that

But Tomonaga, after a day s sightseeing in New

Included the Japanese Pavilion atcontinued with the ship through the Panama Canal
Aboutthe World s

Fair,

and on to Japan.

this Tomonaga said， When I was in Germany I had wanted to stayanother year in Europe, but once I was aboard a Japanese ship I became

7PAGE 88eager to arrive in Japan.
excursion in New York that

He also remarked about hls one day

I found that I was speaking German rather

than English, even though I had not spoken fluent German when I was inGermany．
Tomonaga had returned to Japan with some ideas concerning thequantum treatment of Heisenberg g proposal that attention to strong
field reactions was decisive for understanding the meson‑nucleon
system.

But soon after he began work he became aware, through an

abstract of a paper published in 1939, that Wentzel was also attacking
this problem of strong coupling, Here is where the sclentlfio orbit自of Tomonaga and myself again cross. At about the timethat Tomonaga

returned to Japan I went to California, to work with Oppenheimer. Our
first collaboration was a quantum electrodynamic calculation oftheelectron‑positron pair emitted by an excited oxygen nucleus. And thenwe turned to meson physics,
meson‑nucleon

Heisenberg

hadsuggestedthat

scattering would be strongly suppressed by field

reaction effects.τ'here also existed another proposal to the same end
‑

that

。

the nucleon possessed e玄 cited states, isobars, which would

pr duce almost cancelling
process.

c 。ntrlbutlon•

We showed, classically,thatto the meeon•c 誼 t terlng

the two e玄planatlons ofsuppressed scattering were one and the same:th骨 effect of the strong

field reaction, of the strong coupling, was to produce isobars, boundstates of the meson about the nucleon. The problem of giving theseideas a correct quantum framework naturally arose. And then, we
became aware, through the published paper, ofWentzel's quantum

considerations on a simple model of the strong coupling of meson andnucleon.

I took on the quantum challenge myself. Not liking the way

PAGE 9Wentzel had handled lt, I redid his calculation ln my own style, and,in the process, found that Wentzel had made a mistake.

In th
e

short

note that Oppenheimer and I eventually published, this work of mine ls
referred to aslater,

in a

to be published soon•.

And it was published, 29 years

collection of essa
ys dedicated to Wentzel. Recently,

while surveying Tomonaga a papers, I came upon his delayed publicationof what he had done along the same lines. I then scribbled a note:
Itis as though I were lookin
g at my own long unpublished paper ”•
believethatIboth Tomonaga and I gained from this episode addedexperience in using canonical‑unitary‑transformations to extractthephysical consequences of a theory.
I must not leave the year 1939 without mentioning a work. thatwould loom large

in Tomonaga sstage, I turn back to1937.

later activities.

In this year,

But, to set the

Bloch and Nordsieck.

considered another kind of strong coupllng, that betw
申 告n an electriccharge and arbitrarily soft 申
They

告X

tremely low frequency ‑ lightquanta.

recognized that, ln a collision, say between an electron and anucleus, arbitrarily soft quanta will surely be emitted;
elastic

a perfectly

collision cannot occur. Yet, if only soft photons, those of

low energy, are considered, the whole scattering process goes on as
though theelectrodynamic

interactions were ineffective.

Once thiswas understood, it was clear that the real problem of electrodynamic
field reaction begins when arbitrarily hard ‑ unlimited high energy
photons are reintroduced.
relativistic scatteringspin l/2,

In 1939

Dancoff

performed

such

『

a

calculation both for electrons, which haveand for charged particles without

spin.τ'he spin 0

calculation gave a finite correction to the scattering, but, for spin

9

1
0

PAGE 10l/2, the correction was infinite. This was confusing. And to explain
why that was so, we must talk about electromagnetic mass.
Already in classical physics the electric field surrounding anelectrically charged body carries energy and contributes mass to thesystem.

That mass varies inversely as a characteristic dimension of．τ'he magnetlc

the body, and therefore ls Infinite for a point charge

field that accompanies a moving charge implies an additional momentum,
an additional electromagnetic, mass.

It ls very hard, at this level,

to make those two masses coincide, as they must, in a relativistically．τ'he introduction of relativistic quantum mechanics,

invariant theoryof quantum field theory, changes the situation completely.

For

the

spin l/2 electron‑positron system, obeying Fermi‑Dirac statistics, theelectromagnetic mass, while still
logarithmically, so.

Infinite,

ls

only

weakly,In contrast, the electromagnetic mass for a spin

0 particle, which obeys Bose‑Einstein statistics,

is more singularthan the classical one. Thus, Dancoff a results were ln contradictiontothe expectation that spin 0

shouldexhibitmoresevereelectromagnetic corrections.
Tomonogo s name hod been absent from the Rik.en repor量a for theyears from 1937 to 1939, when he was In Germany.

It reappears for the194•0 spring meeting under the titie On the Absorptlon and Decay of，.Here the simple and important point is made that, when

Slow Meson

cosmic ray mesons are stopped in matter, the repulsion of the nuclear
Coulomb field prevents positive mesons from being absorbed by the
nucleus, while negative mesons would preferentially be absorbed before
decaying.τ'his was published as a Physical Review Letter in 1940.
Subsequent experiments showed that no such asymmetry existed;thePAGE 11

cosmicray meson does notinteract significantly with nuclear

particles.τ'he Rik.en reports from autumn of 1940 to autumn of1942

trace stages in the development of Tomonaga s strong and intermediate
coupling meson theories.

In particular, under the heading

Field

Reaction and Multiple Production there is discussed a coupled set of
equations corresponding to various particle numbers, which ls
basis

of

an

approximation

scheme,thenow generally called theTamm‑Dancoff approximation.τ'his series of reports on meson theory
was presented

to the Meson Symposium ‑ Chuk.anshl Toron
主ai ‑ that was

initiated in September 1943, where also was heard the suggestion of・ group that the cosmic ray meson ls not the meson responsible

Sakata 8

for nuclear forces.
But meanwhile there occurred the last ofheld during the war,

the Rlken meetings

that of spring 1943. Tomonaga provides thefollowing abstract with thetitle

RelatlvisticallyInvariant

Formulation of Quantum Field Theory：

In the present formulation of quantum fields as a
generalization of ordinary quantum mechanics suchnonrelativistic concepts as probability amplitude,
canonical co1Dmutation relation and Schrodinger equation
are used. Namely these concepts are defined referring
to a particular Lorentz frame in space‑time.τ'his
unsatisfactory feature has been pointed out by many
people and also Yukawa emphasized it recently. I madea relativistic generalization of these concepts inquantwn mechanics such that they do not refer to any
particular coordinate frame and reformulate the quantum
theory of fields in a relativistically invariant
manner.
In the previous year Yukawa had commented on the unsatisfactory natureof quantum field theory,
manifestly covariant

pointing both to its lack of an explicit,

form andtothe problem of divergences ‑

1
1

1
2

PAGE 12

infinities.

He. wished to solve both problems at the same time, To

that end, he applled Dirac s

decade earlier suggestionofageneralized transformation function by proposing that the quantum
field probability amplitude should refer. to a closed surface lnspace‑time.

From the graphic presentation of such a surface as acircle, the proposal became k.nown as the theory of maru.

Tomonaga sreaction was to take one problem at a time, and he first proceeded to・reformulate the quantum theory of fi告 lds in a relativistically・

invariant manner. And in doing so he rejected Yukawa 8 more radical
proposal in favor of retaining the customary concept of causality ‑therelation

betweencause and effect,'What was Tomonaga sreformulation?
The abstract I have cited was that of a paper published ln the
Bulletin of the Institute, Rik.en‑Ibo・ But lts contents did not become
known outside of Japan until it was translated into English to appear
in the second issue,that of August‑September,・ 1946, of the newjournal, Progress of Theoretical Physics.

It would, however, be sometime before this issue became generally available in the UnitedStates.

I且 oldentally, ln this 1946 paper Tomonaga gave his address as

Physics Department, Tokyo Bunrlka University. 'While retaining his
connection with Rik.en, he had, in 1941, Joined the faculty of

thisuniversity which later, in 1949, became part of the Tok.yo Universityof Education. Tomonaga begins his paper by pointing out

that

the

standard. commutation relations of quantum field theory, referring to
two points of space at the same time, are not covarlantly formulated:in a relatively moving frame of reference the two points will beassigned different times.τbis is equally true of the Schrodinger

PAGE 13

euation for time evolution, which uses a common time variable fordifferent spatial points.

He then remarks that there is no difficultyin exhibiting commutation r告 Iations for arbitrary space‑time points
whena

non‑interacting

field

is

considered.

τ'heunitarytransror1nation to which we have already referred. now applled to al1
the fields,

providesnon‑interacting

them with thefields,while,

equationsin thein our formulation,themotiontransform
告dequation, only the interaction tenns remain,
says,

or

About

of

Sohrodlnger

this Tomonaga

theory ls divided into two

sections. One section gives the laws of behavior of the fields when
they areleft

alone,and the other gives the laws detennining thedeviation from this behavior due to theinteractions.τ'his way ofseparating the theory can be carried out relativistically • .

Certainly

commutation relations referring to arbitrary space‑time points are
four‑dimensional

in character.

But what aboutthe

Schrodlnger equation, which sti11 retains its single

transformed

time variable?

It demands generalization.
Tomonaga was confident that he had the answer for, as he put it
later，me

I was recalling Dirac s many‑time theory which had enchanted

ten years before，

Dirac‑Fock‑Podolsky,

In thetheory of Dirac,and thenofeach particle is assigned its own time variable.

But, in a field theory, th
色 role of the particles

ls played by thesmall volume elements of space. Therefore, assign to each spatial
volwne element an independent
many‑time

theory・time coordinate.

Thus,

the

"super

Let me be more precise about that idea. At acommon value of the time, distinct spatial volwne elements constituteindependent

physical

systems,fornophysicalinfluencels

13PAGE 141
4

instantaneous. But more than that, no physical influence can travel
fasterthan the speed of light.

that cannot be connected,
independentJ

Therefore any two space‑time regions

even by light signals,

they are said

to be

are physicallyin space‑1ike relationship. A

three‑dimensional domain such that any pair of points ls in space‑like
relationship constitutes a space‑like surface in the four‑dimensional
world. All of space at a common time ls but a particular coordh1ate
description of a plane space‑like surface． Therefore the Schrodinger
equation, in which time advances by aspace,

inshould be regarded as describing the normal displacement of aplane space‑like surface.
changecommon amount everywhereIts

immediate generalization is

to

the

from one arbitrary space‑like surface to an infinitesimallyneighboring one, which change can b唱 localized in the neighborhood ofa given space‑time point.

Such is the nature of the generalized

Schrodinger equation that Tomonaga constructed in 1943, and to which I
came toward the end of 1947.
By thisdominant.
揖time

the dislocation produced by the war became

Much later Tomonaga recalled that

I myself temporarily

toppP.d working on pArticle phy圏 ic自 由fter 1943 and wa圃

electronics research.

Miyazima Tatsuoki

Nishina took me to see several
Research

Institute.

in

Nevertheless the research on magnetrons and on

ultra‑shortwave circuits was basically amechanics.

involved

continuation of quantum

remembers that One day our boss Dr.
engineers at

the Naval Technical

They had been engaged in the research anddevelopment of powerful split anode magnetrons,

andthey seemedtohave come to a concrete conclusion about the phenomena taking place ln
the electron cloud.

Since they were engineers their way of

thinking

PAGE 15

was characteristic of engineers and lt was quite natural that theyspoke in an engineer s way,foreign to me atbut unfortunately it was completely

the beginning.

Every time I met them, I used toreport to Tomonaga how I could not understand them, but he must haveunderstood something,idea of applying the

because after a month or so, he showed me his

Idea of secular perturbation,well‑known incelestial mechanics and quantum theory, to the motion of the el告 ctrons
in the cloud.

I remember that the moment he told me I said

This

ls

・
. Further investigation actually showed that the generation ofitelectromagnetic oscillationsin split anode magnetrons

can

be

essentially understood by applying his idea．
When Tomonaga approachedcircuits, which ls

the problem

ofultra‑shortwave

to say, the behavior of microwaves in waveguides

and cavity resonators, he found the engineers still using the old
language ofimpedance.

He thought this artificial because there nolonger are unique definitions of current and voltage.

Instead,being

a physicist, Tomonaga begins with the electromagnetic field equationsof Maxwel1.

But he quickly recognizes thatthose equations containmuch more information than is needed to describe a microwave circuit.
One usually wants to know only a few things about a typical waveguide
Junction:

if a wave of given amplitude moves into a particular arm,

what are the amplitudes of the waves coming out of the various arms,
including theinitlalone？ τ'he array of all such relations forms amatri玄， even then familiar to physicists as the scattering matrix.

Imention here the amusing episode of the German submarine that arrived
bearing a dispatch stamped Streng Geheim ‑ Top Secret. When delivered
to Tomonaga it turned out to be ‑ Heisenberg s paper on the scattering

1
5

1
6

PAGE 16

matrix,

Coples of thls Top Secret document were soon clrculetlng

among the physicists. Tomonaga preferred to speak. of the scatteringmatrix as the characterlstlc matrix, ln thls waveguideconte玄 t,Hederives properties of that matrix, such as lts unitary character, andshows howvarious experimental arrangements can be described ln termsofthe characteristic matrix of the Junction,

In the paper publishedaftet' the war he r
e
t
t
t
a
l
'
k
s
, concel'ning the utility of
that

＇The

this approach,

final decision, however, whether or not the new concept ismore preferable to impedance should of course be given not only by atheoretical physicist but also by general electro‑engineers・Butperhaps my experience is not irrelevant here,
During the war I also worked on the electromagnetic problems of
microwaves

and waveguides,

I also began with the physicist g

approach, including the use.of the scattering matrix, .But long before
this

three year episode was ended, I was speaking the language of theengineers,

I should lik.e to think that those years of distraction forTomonaga and myself were not without

their useful lessons.τ'hewaveguide inve‑
stlgatlons showed the utility of organizing a theory toisolatethose

inner structural aspects that are not probed under the

given.experimental circumstances, 官
官1at lesson was soon applled in theeffective range description of nuclear forces,

And ltls thisviewpoint that would lead to the quantum electrodynamics conceptofself‑consistent subtraction or renormalization,
fomonaga already understood theimportance ofdescribing

relatlvlstlc situations convarlantly ‑ without specialization to any
particular coordinate system. At about thls tlme, I began tothatlesson pragmatically,learn

in the context of solving a physicalPAGE 17problem. As the war

ln Europe approached lts end,

the American

physicists responsible for creating a massive microwave technology
began to dream of high energy electron accelerators.
practical

One ofquestions involved ls posed by the strong radiation emitted

by relativistic electrons swinging ln circular orbits.
what

the

In studying

ls now called synchrotron radiation, I used the ractlon of the

field created by the electron's motion. One part ofdescribes

that reaction

the energy and momentum lost by the electron to theradiation.τ'he other part ls an added inertial
by an electromagnetic mass.

effect characterized

I have mentioned

the relativistic

difficulty that electromagnetic mass usually creates.
covariant method

I was using,in thebased on action and proper time, aperfectly invariant form emerged. Moral:
result use a

But,

to end with an invariant

covariant method and maintain covariance to the end of

the calculation.

And,

in

the

appearanceofaninvariantelectromagnetic mass that simply added to the mechanical mass to form
the physical mass of the electron,

neither piece being separately

distinguishable under ordinary physical circumstances, I was S申 eingagain the advantage of isolating unobservable structuralthetheory.

aspects of

Looking back. at lt, the basic ingredients of the coming

quantum electrodynamic revolution were now ln place.

Lacking was anexperimental impetus to combine them, and take them seriously.
Suddenly, the Pacific War was over.
TolDonaga reestablished his seminar.
brewing in Sakata S Nagoya group.

Amid

total

desolation

But meanwhile, something had been

It goes back to a theory of Moller

and Rosenfeld, who tried to overcome the nuclear force difficulties ofmeson theory by proposing a mixed field theory, with both pseudoscalar

1
7

1
8

PAGE 18

and vector mesons of equal m
a
s
1
1
1
.

I like to think. that my modificationof this theory, in which the vector meson is more massive, wasprediction of

the later discovered ‑meson.

theSomewhat analogously,

Sakata proposed that the massless vector photon ls accompanied by amassive scalar meson called the cohesive or C‑meson. About this,Tomonaga said，ln 1946, Sakata proposed a promising method of

eliminating the divergenc骨ofthe electron mass by Introducing theidea of a field of cohesive force.

It was the idea that there exists

an unknown field, of the type of th
申 meson field, which interacts withthe electron ln addition to the electromagnetic field.
this

field

the

cohesive

force

Sakata named

field. because the apparent

electromagnetic mass due to the interaction of this field andelectron,thethough Infinite, is negative and therefore the e玄 lstence of

this field could stabilize the electron in some sense. Sakata pointed
out the po軍 slbility that the electromagnetic mass and the negative new
mass cancel each other and that the infinity could be eliminated bysuitably choosing the coupling constant between this field and theelectron. Thus the difficulty which had troubled people

。

for a

long

・
. Let etime seemed to disappear insofar as the mass was o noerned
break in here and remark that this solution ofproblem is,in fact,

illusory.

the mass divergence

In 1950, Kinoshita showed that thenecessary relation between the two coupling constants would nocancel四longerthe divergences, when the discussion ls extended beyond thelowest order of approximation,

Nevertheless,

the C‑meson hypothsisserved usefully as one of the catalysts that led to the introductionof the self‑consistent subtraction method. How that came about
described

in Tomonaga s ne玄 t sentence2

isThen what concerned me most

PAGE 19

was whether thelnflnltles appearing in the electron scattering

process

also

could

be removed by theidea of a plus‑minus

cancellation.
I have already referred to the 1939 calculation of Dancoff,radiative corrections

onto electron scattering, which gave an lnfinlte

result. Tomonaga and his collaborators now proceeded to calculate theadditional

effect of the cohesive force field.

divergent results of the opposite sign, but
cancel Dancoff s

infinite

It encouragingly gave

they did not precisely

terms.τ'his conclusion was reported in a

letter of November 1, 1947, submitted to the Progress ofPhysics,

Theoreticaland also presented at a symposium on elementary particles

held in Kyoto that same month. But meanwhile parallel calculations oftheelectromagnetic

effect were going on,

calculations, which were not
reproduced Dancoff s

result.

reported

repeating Dancoff sln detail.

At

first

they

But then Tomonaga suggested a new andmuch more efficient method of calculation.

It wasto usethecovariant formulation of quantum electrodynamics, and subject lt to aunitary transformation that immediately isolated

the electromagnetic

mass term. Tomonaga says,

Owing to this new, more lucid method, we noticed thatamong the various terms appearing ln both Dancoff s andour previous calculation, one term had been overlooked.
There was only one missing term, but it was crucial to
the final conclusion. Indeed, if we corrected thiserror, the infinities appearing in the scattering
process of an electron due to the electromagnetic andcohesive force fields cancelled completely, except forthe divergence of vacuum polarization type.
A letter of December 30,
announcement.

1947,

corrected the previous erroneous

1
9PAGE 20

20

But what is meant by the divergence or vacuum polarization
type？

From the beginning of Dirac s theory of positrons it had beenrecognized that, ln a sence,
medlmn;the vacuum behaved as a polarlzable

the presence of an electromagnetic field induced a charge

distribution acting to oppose the inducing field.

As aconsequence

the charges of particles would appear to be reduced, although theactual calculation gave a divergent result. Nevertheless, the effectcould be absorbed
charge.

At

into athis stage,

redefinition,a r色 normalization, of thethen, Tomonaga had achieved afinltecorrection to the scattering of electrons, by combining two distinct
ideas:
ofthe renormalization of charge, and the compensation mechanism

the C‑meson field.

developing.

But meanwhile another line of thought had been

In this connection let me quote from a paper, publish邑 d

at about this time, by Taketani Mltsuo:，．τ'he present state of theoretical physics ls confronted
with difficulties of extremely ambiguous nature.τ'hese
difficulties can be glossed over but no one believes
that a definite solution has been attained. The reason
for this is that, on one hand, present theoreticalphysics itself has logical difficulties, while, on theother hand, there ls no decisive experiment whereby t
determine this theory uniquely.

。

雌In June of 1947 those decisive experiments were made known,in theUnited States.
For three days at the beginning of June, some twenty physicists
gathered at Shelter

Island,located in a bay near the tip of Long

Island, New York. There we heard the details of

the experiment bywhich Lamb and Retherford had used the newmicrowave techniques toconfirm the previously suspected upward displacement of the 2S level

PAGE 21of hydrogen. Actually, rumors of this had already spread, and, on the
train to New York, Victor Weisskopf and I
electrodynamic

effects

were

involved,

andcalculation would give a flnlte prediction.
totally

unexpecteddisclosure,

had

agreedthat aBut

that

relativistic

there was also a

by Isador Rahl:

the hyperflne

structures in hydrogen and deuterium were larger than anticipated by afraction of a percent. Here was another flaw ln the Dirac electron
theory, now referring to magnetic rather than electric properties.
Weisskopf and I had described at Shelter Island ourtherelativistic electron‑positron theory,idea

then called

theory, would produce a finite electrodynamic energy shift.

thatthe hole
Butlt

was Hans Bethe who quickly appreciated that a first estimate of thiseffect could he found without entering into
relativistic calculation.

the complications of

8

In a Physical Review article received onJune 27, he says,

Schwinger and Weisskopf, and Oppenheimer havesuggested that a possible explanation might he theshift of energy levels by the interaction of theelectron with the radiation field. This shift comesout infinite in all existing theories, and has
therefore always been ignored. However, it ls possible
to identify the most strongly (linearly) divergent termin the level shift with an electromagnetic mass effectwhich must exist for a bound as well as a freeelectron. This effect should properly be regarded asalready included in the observed mass of the electron,
and we must therefore subtract from the theoreticalexpression, the corresponding expression for a freeelectron of the same average kinetic energy. The
result then diverges only logarlthmically (instead of
1inearly) in non‑relativistic theory; Accordingly, it
may be expected that in the hole theory, in which themain term (self‑energy of the electron) diverges only
logarithmically, the result will be convergent after
subtraction of the free electron ex
pression. This
would set an effective upper limit of the order of
mc to the frequencies of light which effectively
contribute to the shift of the level of a bound

2
1

PAGE 2222electron. I have not carried out the relativistic
calculations, but I shall assume .
th11t such an effective
relativistic limit exists.
The outcome of Bethe g calculation agreed so well with thethen notvery accurately measured level shift that there could b骨 no doubt of
its electrodynamic nature.

Nevertheless, the relativistic problem, of

producing a flnlte and unique theoretical prediction, still remained.
The news of the Lamb‑Retherford measurement and of Bethe snon‑relativistic calculation reached Japan in an unconventional way.
Tomonaga says,"The first information concerning the Lamb shift was
obtained not through the Physical Review, but throughthe popular science column of weekly U.S. magazine.
This information about the Lamb shift prompted us tobegin a calculation more exact than Bethe s tentative
one."

・

He goes on:
In fact, the contact transformation method could beapplied to this case, clarifying Bethe s calculationand justifying his idea. Therefore the method ofcovariant contact transformations, by which we did
Daucoff s calculation over again would also be usefulfor the problem of performing the relativistic
colculotlon for the Lamb shift.
Incidentally, ln speaking of contact transformations Tomonaga ls using
another namefor canonicalor unitary transformations. Tomonaga

announced his relativistic program at

the already mentioned .Kyoto

Symposium of November 24‑25, 1947. He gave lt a name, which appears
in the title of a letter accompanying the one of December 30 thatpoints out Dancoff s

error.τ'his

title is・Application of theSelf‑Consistent Subtraction Method to the Elastic Scattering of an
Electron'. And so, at the end of 1947 Tomonaga was in full possession

PAGE 23of the concepts of charge and mass renormalization.
Meanwhile, immediately following the Shelter Island Conference
I found myself with a brand new wife, and for two months we wanderedaround the United States.

Then lt was tlme to go to work again,I

also clarified for myself Bethe S

nonrelatlvlstic calculation by

applying a unitary transformation thatisolated the electromagnetic

mass. This was the model for a relativistic calculation, based on theconventional hole theory formulation of quantum electrodynamics.
here

I held an unfair advantage over Tomonaga, for, owing to th色

communication problems of the time, I knew that there wereof experimental effects
and

But

to be explained:

the magnetic one of Rabi.

two kinds

the electric one of Lamb,

Accordingly,

I carried out

acalculation of the energy shift in a homogeneous magnetic field, whichis the prediction of an additional magnetic momentofthe electron,

and also considered the Coulomb field of a nucleus in applications tothe scattering and to the energy shift of bound states.
were described in a

letter to

The results

the Physical Review, received on

December 30, 1947, the very same date as Tomonaga s proposal

of

the

self‑consistent subtraction method.τ'he predicted additional magnetic
moment accounted for the hyperfine structure measurements,forlater, more accurate,

and also

atomic moment measurements. Concerning，・,,the finite radiative correction to the elastic

scattering I said

scattering of electrons by a Coulomb field provides a satisfactorytermination to a subject that has been beset with much confusion".
Considering the absence of experimental data, this is perhaps all thatneeded to be said. But when lt came to energy shifts,
was,

what

I wrote23

2
4

PAGE 24The values yielded by our theory differ only slightly
from those conjectured by Bethe on the basis of anon‑relatlvlstlc calculation, and are, thus, ln goodaccord with experiment.
Why did I not quote a precise number?
τ'he answer to that was given in a lecture before

the American

Physical Society at the end of January, 1948. Q.
ulte simply, something
was wrong. The coupling of the electron spin to
was numerically different
would lmply1

relativistic

non‑covariant calculation.

from what the additional magnetic moment
invariance
One could,

coupllng to have the right value and,shift

the electric fieldwasviolatedin

thisof course, adjust that spinin fact,

the correct energy

is obtained ln this way. But there was no conviction in such a

procedure. The need for a covariant formulation could no longer beignored.

At the time of this meeting the covariant theory had alreadybeen constructed, and applied to obtain an invariant
the electron electromagnetic mass.

expression forI mentioned this briefly.

Afterthe talk, Oppenheimer told me about Tomonaga's prior work.
A progress report on the covariant calculations,
technique ofusing theinvariant par呂 田eters, wa自 presented at the Poco且 O Ha且 or

Inn Conference held March 30 ‑ April

1,

1948.

At

that very time

Tomonaga was writing a letter to Oppenheimer which would accompany acollection of manuscripts describing the work of his group.
response,

Oppenheimer sent a telegram：

In

Grateful for your letter andpapers. Found most interesting and valuable mostly paralleling muchwork done here.

Strongly suggest you write a summary account ofpresent state and views for prompt publication in Physical Review.
Glad to arrange.

On May 28, 1948, Oppenheimer acknowleges the receipt

PAGE 25of Tomonage s letter entitled On lnflnite Field Reactions in Quantum
Field Theory
・He writes，騎 Your very good letter came two days ago

and today your manuscript arrived.

I have sent it on at once

to

the

Physical Review with the request that they publlsh it as promptly as
possible•••I also sent a brief note which may be or some interest to

you in the prosecution of higher order calculations.

Particularly in

the identification of light quantum self energies, it proves important
to apply your relativistic methods throughout, We shell try to get an
account of Schwinger s work on this and other subjects to you in thevery near future ・He ends

theletter e玄 pressing the "hope that

before long you wi11 spend some time wlth us at the Instltute where weshould all welcome you so warmly．
The point of Oppenheimer g added note ls

this:

In examining

the radiative correction to the Klein‑Nishina formula, Tomonaga andhis collaborators had encountered a
involved

divergence additional

in mass and charge renormalization.

as a photon mass.

But unlike

electron, which can be

the electromagnetic mass ofamalgamated,

ls no photon massequations.

notes

the possibility of atoidea of Sakata.

analogous

the

the

as Tomonaga put it, Into an

there

cancellation,

those

It could be identified

already existing mass,
Tomonaga

toin the Maxwell
compensationIn

response,

Oppenheimer essentially quotes my observation that a gauge invariant
relativistic theory cannot have a photon mass and further,sufficiently careful

that

a

treatment would yield the required zero value.

But Tomonaga was not convinced.

In a paper submitted about thistime

he speaks of the somewhat quibblin
g way in which it was argued thatthe photon mass must vanish. And he was right, for the real

subtlety

25

PAGE 26

2
6

underlying the photon mass problem did not surface for another 10
years,

in the eventual recognition of what others would

call

schwlnger terms'.
But even the concept of charge r骨normalization was troubling tosome physicists.

Abraham Pais, on Aprl1 13, 1948, wrote a letter toTomonaga in which, after commenting on his own work parallelto thatof Sakata, he remarks, "lt seems one of the most puzzling problems how

・

to renormalize the charge of the electron and of the proton in sucha way as to make the experimental values for these quantities equal toeach other•.

PeE・
haps 1 was the first to fully appreciate that charge

renormalization is a prop邑 T ty ofthe electromagnetic field alone,which results in a renormalization, a fractional reduction of charge,
that is the same for all. But while E m congratulating myself, I mustalso mention a terrible mistake I made. Of course, I wasn t entirely
alone ‑ Feynman did it

too・It occurred in the relativistic

calculation of energy values for bound states.
energy photons was treated covariantlyl

The effect of highthat of low energy photons in

the conventional way. These two parts had to he Joined together,asubtlely

involved

inrelating

theandrespective four‑ andthree‑dimensional treatments was overlooked for several months.

But

sometime around September, 1948, it was straightened out, and, apartfrom some uncertainty about
effects,

the inclusion of vacuum polarization

all groups, Japanese and American, agreed on the answer. As

I have mentioned, it was the result I had reached many months before
by correcting the obvious relativistic error of my first non‑covariant
calculation.
In that same month of September,

1948, Yukawa, accepting an

PAGE 27

lnvltatlon of Oppenheimer, went to the Instltute for Advanced Study at．τ'he letters that he wrote back. to Japan werePrinceton, New Jersey
circulated in a

new informal

Journalcalled Elementary Particle

Physics Research ‑ Soryushiron Kenk.yo. Volume 0 of that Journal
containsalso

the communications of Oppenheimer and Pals to which I havereferred, and a letter of Heisenberg to Tomonaga,
Heisenberg s

paper,

inquiring whether

sent during the war, had arrived.

In writing toTomonaga on October 15, 1948, Yuk.awa says, ln part， Yesterday I met
Oppenheimer, who came back from the Solvay Conference. He thinks very
highly of your work. Here, many people are interested in Schwinger s
and your work. and I think that this ls the main reason why the demand
for the Progress of I'heoretlcal Physics ls high.

I am very happy

about this．
Duringtheperiodofintenseactlvltyinquantum

electrodynamics, Tomonaga was also Involved ln cosmic ray research.
The results of a collaboration with Hayakawa Satlo were publishedln1949 under the title Cosmic Ray Underground . By now, the two mesons
and．τ'his paper discusses thethe subsequenteffects produced by, the deep

had been recognized and named:
generation of,penetrating

andmeson. Among other activities in that year of

Tomonaga publishedabook on quantum mechanics that would be quite

influential, and he accepted Oppenhelmer slnstltute

1949,

for Advanced Study.

lnvltatIon to visIt

theDuring the year he spent there heturned in a new direction, one that would also interest me a number ofyears

later.

Itisthe quantum many‑body problem. The resulting

publication of 1950 Is entitled Remarks on Bloch's Method of Sound
Waves Applied

to Many‑Fermion Problems . Five years later he would

27

PAGE 282
8

generalize this ln a study of quantum collective motion.
But the year of enormous scientific productivity were coming toa close, owing to the mounting pressures of other obligation.

In 1951

Nishina died, and Tomonaga accepted his administrative burdens.
Tomonaga gattention turned

facilities

availabletoNow

toward improving the circumstances andyoungerscientists,

establishment of new Institutes and Laboratories.

includingthe

In 1956 he became

President of the Tokyo University of Education, which post he held forsix years.τ'hen, for another six years, he was President of Science
Council of Japan, and also, in 1964, assumed
Nishina Memorial Foundation.

The

the

I deeply regretted that he was unable tobe with us in Stockholm on December 10,
Prize.

the Presidency of1965 to accept his Nobel

lecture that I have often quoted today was delivered May

6, 1966.
Following his retirement in 1970, he began to write anothervolume of his book. on quantum mechanics which, unfortunately, was notcompleted. Two other books, one left in an unfinished state, were
publised, however.

To some e玄 tent, these books are directed to thege且 eral public rather than the p
r
o
f
e
:
1
1
:
1
1
l
o
n
a
l:
1
1
c
l
e
n
t
l
:
1
1
t
.
Tomonaga and I found acommon path.

A且 d here again

I have recently completed aseries of television programs that attempt to explain relativity to
the general public.

I very much hope that this series, which was

expertly produced by the British Broadcasting Corporation, will
eventually be shown in Japan.
Just a year ago today, our story came to a close. But Tomonaga
Sin‑itiro

lives on in the minds and hearts of the many people whose

lives he touched, and graced.