CBPF-CS-012/97
Richard Feynman to Enrico Fermi:
a letter from Rio de Janeiro, 1951
J. Leite Lop es
Centro Brasileiro de Pesquisas Fsicas - CBPF
Rua Dr. Xavier Sigaud, 150
22290-180 - Rio de Janeiro-RJ, Brazil
and
Universidade Federal do Rio de Janeiro
Richard Feynman came to Rio de Janeiro for the rst time in 1949. The Centro
Brasileiro de Pesquisas Fsicas | CBPF | had just b een founded by a group of Brazilian
physicists led by Cesar Lattes | who had contributed in 1947 to the discovery of pions
| and mathematicians led by Leop oldo Nachbin and Maurcio Mattos Peixoto, in order
to promote researchworkincontemp orary themes of physics and help in the university
education of physicists.
Feynman liked the atmosphere at the Centro and was attracted by the city and its
b eaches. He came backayear later and stayed during his U.S. Sabbatical year, 1951 -
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1952. He gave lectures at the University and at the Centro on electro dynamics and was
working an meson theory after his well-known success in quantum electro dynamics. He
prop osed to me that weinvestigate whether the symmetrical pseudoscalar meson eld
theory could give a description of the deuteron which could b e exp erimentally checked, in
1
spite of the dicultyofthe -singularity at the origin of the tensor-force in the Yukawa
3
r
4
p otential. Feynman comments this work in his letter to Fermi in the p ort-scriptum P S .
The results of this research are in a pap er published in the Pro ceedings of a Symp osium
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whichwas held in Rio and which I presented after Feynman left for Japan in May 1952.
Feynman enjoyed very much his stay in Rio and came back during his summer vaca-
tions several times. In 1953, he had his ideas on sup erlfuidity in our city.Ashesays in
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Details of his activities anf feelings in Rio may b e found in the pap er J. Leite Lop es, RichardFeynman
in Brazil: recol lections, QUIPU, Revista Latino-Americano de Historia de las Ciencias y la Tecnologia,
vol. 7 numero 3, Mexico (1990)
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J. Leite Lop es and R.P.Feynman, On the pseudoscalr meson theory of the deuteron New Research
Tecniques in Physics, Academia Brasileira de Ciencias, Rio de Janeiro (1954)
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this letter to Fermi: \(I) am going to the Copacabana b each to see if I can get one (ideas)
of myown. I get lots of ideas at the b each."
It was a great joy for me to work and discuss with him. Wewere together in Pasadena,
at Caltech, during the year 1956-1957 and in Mexico City in 1972 where we discussed on
the emerging gauge eld theories and nally in 1977 when I invited him to come to Stras-
b ourg and present a review pap er on the parton mo del to an International Symp osium
on multiparticle dynamics whichwas held in the charming Alsacian town of Kaysersb erg,
birthday of Alb ert Schweitzer.
Here is Feynman's letter to Enrico Fermi:
Rio de Janeiro
Decemb er 19, 1951
Dear Fermi,
Being thousands of miles awayIhave only heard by amateur radio from friends in the
U.S. that you are doing exp eriments in meson scattering from protons. I don't know what
your theoretical friends are saying, so I should liketomakesomecoments at the risk of
only saying what is obvious to everyb o dy in the U.S.
To b egin with I am of the opinion that Yukawa's meson theory with pseudoscalar
mesons gradient coupling, is wrong, (or least useless) in its present form | b ecause at
least p erturbation theory is N.G. and otherwise divergences cloud the issue. But I think
3
mesons are pseudoscalar, and I think the amplitude that a nucleon emits just one may
b e prop ortional to .Q (where is the nuclear spin, Q the meson momentum) for Q
small. (This is of course in agreement with the Yukawa theory | to all orders in account,
H H HHH
f
i
b ecause for low Q one op erator in the series H + + etc. is prop ortional
fi
E E E
i
to Q and others, involving all the virtual mesons are not (the virtual moments are of
order , the meson mass) so for Q low enough the sum will b e prop ortional to Q, and
further will b e Qtimes the sum with the op erator in place of one of the H's | which
1
means Q.times a spin ob ject which can only therefore b e prop ortional to ). Let us say
2
1
then the coupling is G(Q)( Q)u for emission of one meson amplitude u, momentum
Q, mass where G(Q) is a function of Q (and p ossibly the nucleon moments at higher
Q??) and I exp ect G to have the prop erties of not varying muchfor Q small, just is a
3
Imake all analyses thinking of the theory non-relativistic in the nucleons.
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reasonable function of Q=.For Q =0,callG(O )=G (If p ert theory were OK G is just
0 0
the usual g ). Further this is most reasonale on nearly any theory | for the meson b eing
pseudoscalar the co ef to emit one (even if proton is a p ositron + 18 neutrinos + 4 neutral
mesons) must b e ps.scalar | which , if it do esn't involvethenucleon momenta (and I
can't see how it easily can b e galilean invariant | but Nature's imagination always has
my resp ect) can hardly b e other than Q. (According to Yukawa theory, standard form,
2
the total series would givea G(Q)which, if g were very small and integrals converged,
2
would b e nearly constant for all Q andequaltog | but if g is larger, correction terms
set in for Q of order ).
I wish to app eal to exp eriment to try to establish, if p ossible, wheter the ab oveis
correct and the coupling is like Q for one meson absorption. You see tho I mean only
to refer to low energy mesons |for Q or higher I have no arguments ab out what to
exp ect.
Yet it is imp ossible to measure the absorption of one meson bynucleon directly for
the conservation of energy demands that another coupling enter to take out the energy.
If we do it with a -ray, or a collision b etween nucleons new uncertainties arise, but if we
do it by means of another meson (scattering) the situation would app ear to b e as simple
as p ossible.
The \intermediate states" (if they mean anything) have, mayb e, energy of order
so that as long as Q remains small enough (non-rel. mesons) the intermediate states do
not dep end muchon Q. Then, if we assume the coupling for two mesons is essentially like
the double action of the lst order coupling, we see that the matrix element for scattering
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ought to b e prop ortional bilinearly to Q and Q .Itmust therefore have the form
1 2
M = X Q Q + X i (Q Q )
1 1 2 2 1 2
of if Q ;Q lie in x; y plane at angle one to other using c.g. system Q = Q = Q
1 2 1 2
2
M = Q (x cos + i sin X )
1 2
where X ;X are some functions of Q, insentitiveto Q for small Q. But in principle
1 2
knowledge of the coupling of one meson do es not determine that for two. There could
still b e a term with arbitrary co ecient in the Hamiltonian of form u u which is scalar.
1 2
Hence we mightexpect
2
M = Q (X cos + i sin X )+X
1 z 2 3
(For example, gradient and direct coupling theories agree on Q for one meson, but
for two X is very di erent b eing very small for grad. and very large for direct- in p ert.
3
theory).
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Because, if you like, now in the p ert series one of the H is prop. Q , other to Q and otherwise
1 2
nothing is sensitivetothevalues of Q ;Q .
1 2
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Naturally such a form is completely general | but what I wanttoverify is that
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X is very small (mayb e order =M smaller than X ;X); (1)
3 1 2
(could in principle dep end on spin | I will assume it do esn't)
2 2 2
X ;Xare insensitiveot Q for Q well b elow : (2)
1 2
I am not in p osition to calculate X ;X in terms of G, nor to get a relation b etween
1 2
them | for wehave no go o d theory. (One p ossibility of course is that relations of the lst
order p ert theory may b e true, but let us rst nd out if (1), (2) are true and that b eing
established go on from there.)
Coments: (1) is a pure guess | various evidence (suchas emission comp eting
0
favorably with emission in H capturing ) indicates it is so | all the evidence which
is usually aduced to prefer the grad. to direct coupling is just a question of how big X
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is. I assume for no excellent reason that X do es not dep end on spins.
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(2) could b e wrong. It would b e very interesting. For it probably would mean there
exist imp ortant\intermediate states" at low (rel. to ) energy | whichwould b e a vital
discovery. Hence I urge you to try to see whether the predictions of (1), (2) are satis ed.
Incidentally since M for the inverse reaction should b e the complex conjugate I con-
0
clude all X s are real (but I am notoriously punk at such arguments | get a eld theory
or group theory exp ert).
0
Next, very interesting is the relation of the X s for di erent reactions (I mean mesons
of di erentcharges, neutral etc.). It would b e very interesting if we could verify that the
symmetric theory is valid. Let us lo ok at the predictions of this theory for this problem
and test it later exp erimentally.If~u; ~v are the vectors in isotopic spin space representing
the mesons in and out, and is the op erator for the nucleon M must b e bilinear in u,
and v and invariant in isotopic spin, or of the form
M = A(~u~v )+Bi~ (~u ~v ) (3)
where A; B are matrices involving spin etc. (Whichwe later write in the form
A = A + i A ; (4)
1 z 2
B = B + i B (5)
1 z 2
and we exp ect nearly to write
2 2
A = Q X cos + X , A 2Q X sin
1 1 3 = 2
2 2
B = Q Y cos + Y , B = Q Y sin ; X ;Y
1 1 3 2 2 3 3
small, X; Y nearly constant
2
small Q . All real?
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but form (3) do es not dep end on assumptions (4) (5) of course, just invariance.).
That is, getting down to cases, the matrix element for each pro cess is given in the
following table. Pro cesses lab eled with the same \TYPE" letter have equal probabilities
|aswould b e exp ected from either reaction-inverse or the most naive use of the charge
+ 0
symmetry idea: is to p as is to n and is impartial.
Now let us lo ok at the X -sect for various cases. In complete generality. A can b e
written in the form A = A + i AA where A is scalar AA is 3 quantities (complex)
1 0 2 1 2
(vector) and B = B + i IB . Summing over all spin directions of the nucleon then we
1 2
obtain that the cross section is prop ortional in each case resp ectively to,
2 2
PROCESS ELEMENT TYPE (a) jA + B j + jAA + IB j
1 1 2 2
+ + 2 2
+ p ! + p A + B (a) (b) 2(jB j + jIB j )
1 2
p
0 +
+ p ! + n 2 B (b)
0 2 2
! + p A (c) (c) jA j + jAA j
1 1
p