Selected Papers On Gauge Theory Of Weak And Electromagnetic Interactions

237 Pages·1981·18.453 MB·English

by  C. H. Lai (Editor)

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World Scientific Singapore
1981
World Scientific Publishing Co. Pte Ltd CONTENTS
P. O. Box 128
Farrer Road
Singapore 9128
Preface
1979 Nobel Lectures
S. Weinberg, "Conceptual foundations of the unified theory of
Editorial Advisory Committee weak and electromagnetic interactions".
H. Araki (Kyoto)
A. Salam, "Gauge unification of fundamental forces".
S. S. Chem (Berkeley)
R. Dalitz (Oxford) S. L. Glashow, "Towards a unified theory: Threads in a tapestry".
K. Huang (MIT)
M. Jacob (CERN)
T. D. Lee (Columbia) /. Yang-Mills Field and Early Attempts to Unify Weak and Electro
M. J. Moravcsik (Oregon) magnetic Interactions
A. Salam (Trieste)
C. N. Yang (Stony Brook) 1. C. N. Yang and R. L. Mills, Phys. Rev. 96, 191 (1954),
"Conservation of isotopic spin and isotopic gauge in variance".
2. J. Schwinger, Ann Phys. (N.Y.) 2, 407 (1957) "A theory of
the fundamental interactions".
3. A. Salam and J. C. Ward, Nuovo Gmento 19, 165 (1961),
"On a gauge theory of elementary interactions".
4. S. L. Glashow and M. Gell-Mann, Ann Phys. (N.Y.) 15, 437
(1961), "Gauge theories and vector particles".
This volume consists of selected papers on the Gauge Theory of Weak
and Electromagnetic Interactions that have appeared in Annals of
Physics, IL Nuovo Cimento, Nuclear Physics B, Physics Letters B, //. Spontaneous Symmetry Breaking and Goldstone's Theorem
Physical Review, Physical Review Letters and Theoretical and Mathe
matical Physics. Included also are the 1979 Physics Nobel Lectures and 5. J. Goldstone, Nuovo Cimento 19, 154 (1961), "Field theories
an article by Prof. A Salam from the Proceedings of the Eighth Nobel with superconductor solutions".
Symposium on Elementary Particles Theory published by Almqvist &
Wiksell Forlag AB. The editor and publisher are indebted to the original 6. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961),
authors, journals, Nobel Foundation and other publishers for their "Dynamical model of elementary particles based on an analogy
assistance and permission to reproduce these papers.
with superconductivity".
7. J. Goldstone, A. Salam and S. Weinberg, Phys. Rev. 127,
965 (1962), "Broken symmetries".
///. Spontaneous Breaking of Local Gauge Symmetries and Higgs
Mechanism
8. P. W. Higgs, Phys. Lett. 12, 132 (1964), "Broken symmetries,
Copyright © 1981 by World Scientific PubUshing Co Pte Ltd massless particles and gauge fields".
ISBN 9971-83-023-x 9. F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964),
ISBN 9971-83-022-1 pbk "Broken symmetry and the mass of gauge vector bosons".
10. G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. 24. J. C. Taylor, Nucl. Phys. B33, 436 (1971), "Ward identities
Rev. Lett. 13, 585 (1964), "Global conservation laws and and charge renormalization of the Yang-Mills field."
massless particles". 130
25. A. A. Slavnov, Theo. Math. Phys. 10, 99 (1972), "Ward
11. P. W. Higgs, Phys. Rev. 145, 1156 (1966), "Spontaneous identities in gauge theories".
symmetry breakdown without massless bosons". 133
12. S. Weinberg, Phys. Rev. D7, 1068 (1973) "General theory Renormalization of Gauge Theories
of broken local symmetries". 141 26. G. 't Hooft, Nucl. Phys. B33, 173 (1971), "Renormalization
of massless Yang-Mills fields".
13. J. S. BeU, Nucl. Phys. B60, 427 (1973), "High-energy
behavior of tree diagrams in gauge-theories" 156 27. G. 't Hooft, Nucl. Phys. B35, 167 (1971), "Renormalizable
14. C. H. Uewellyn Smith, Phys. Lett. 46B, 233 (1973), "High Lagrangians for massive Yang-Mills fields".
energy behavior and gauge symmetry". 166 28. G. 't Hooft and M. Vdtman, Nucl. Phys. B44, 189 (1972),
"Regularization and renormalization of gauge fields."
IV. The Standard Model
29. B. W. Lee and J. Zinn-Justin, P/i^^s. Rev. D5, 3121 (1972),
15. S. L. Glashow, Nucl. Phys. 22, 579 (1961), "Partial-Symmetries "Spontaneously broken gauge symmetries. I. Preluninaries".
of weak interactions". 171 30. B. W. Lee and J. Zinn-Justin, Phys. Rev. D5, 3137 (1972),
"Spontaneously broken gauge symmetries. 11. Perturbation
16. A. Salam and J. C. Ward, Phys. Lett. 13, 168 (1964),
"Electromagnetic and weak interactions". 181 theory and renormalization".
17. S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967), "A model 31. B. W. Lee and J. Zinn-Justin, i'/z;;^ Rev. D5, 3155 (1972),
"Spontaneously broken gauge symmetries. 111. Equivalence".
of leptons". 185
32. B. W. Lee and J. Zinn-Justin, Phys. Rev. D7, 1049 (1973),
18. A. Salam, in "Elementary Particle Theory", ed. N. Svartholm
"Spontaneously broken gauge symmetries. IV. General gauge
(Almqvist and Wiksell, Stockholm, 1968), "Weak and electro
formulation".
magnetic interactions". 188
19. S. Weinberg, Phys. Rev. Lett. .27, 1688 (1971), "Physical 33. D. A. Ross and J. C. Taylor, Nucl. Phys. B51, 125 (1973),
processes in a convergent theory of the weak and electro "Renormalization of a unified theory of weak and electro
magnetic interactions". 199 magnetic interactions".
20. S. L. Glashow, J. lUopoulos and L. Maiani, Phys. Rev. D2, 34. C. Becchi, A. Rouet and R. Stora, Ann. Phys. (N.Y.) 98,
287 (1976), "Renormalization of gauge theories".
1285 (1970), "Weak interactions with lepton-hadron symmetry". 203
V. Quantization of Gauge Fields, Feynman Rules
21. L. D. Faddeev and V. N. Popov, Phys. Lett. 25B, 29 (1967),
"Feynman diagrams for the Yang-Mills field". 211
22. V. N. Popov and L. D. Faddeev, Kiev Report No. ITP-67-36
(1967); English translation by D. Gordon and B. W. Lee,
NAL-THY-57 (1972), "Perturbation theory for gauge invariant
fields". 213
iS; 23. K. Fujikawa, B. W. Lee and A. I. Sanda, Phys. Rev. D6,
2923 (1972), "Generalized renormalizable gauge formulation
of spontaneously broken gauge theories". 234
P R E F A CE
JHIS VOLUME of selected papers is not meant to serve as
an introduction to the gauge theory of weak and electromagnetic
interactions. Rather, the purpose of its publication is to provide
physicists new to the field, particularly those in developing
countries, with a compilation of some of the original literature,
which are scattered in various journals and over many years.
For the seasoned worker, this collection could perhaps still serve
as a handy reference. The importance of the concept of gauge
theories can hardly be exaggerated these days, and it is hoped
that this volume will be consulted not only for the technical
details but also to gain some flavor of the logical development
of many of the ideas and techniques involved.
Many good summer school lectures and review articles exist
and should be consulted for a coherent introduction. We find
the following particularly useful:
C. Quigg, "Introduction to Gauge Theories of the Strong,
Weak and Electromagnetic Interactions", Lectures given at
the NATO Advanced Study Institute, "Techniques and
Concepts of High Energy Physics", held at St. Croix, U.S.
Vkgin Islands, July 2-13, 1980. (Available as FERMILAB-
Conf-80/64 THY)
J. C. Taylor, "Gauge Theories of Weak Interactions",
Cambridge University Press, 1976.
E. S. Abers and B. W. Lee, "Gauge Theories", Physics
Reports 9C, 1 (1973).
vii
Preface
The Nobel lectures by the 1979 Laureates, Professors S. L.
Glashow, A. Salam and S. Weinberg, are reprinted here: We
feel that they provide interesting (if highly personal) accounts
of the evolution of our present understanding of the electroweak
interactions, as well as some ideas on the current outlook.
This selection of papers is not complete nor definitive by
any standard and hence is far from giving proper credit to all
contributions. Limitation of space, considerations as regarding
the usefulness of the volume, and our limited expertise in the
field have been deciding factors m the compilation. We apologize
for any deserving papers that we have wittingly or unwittingly
omitted. Two remarks about the sections on quantization and
renormalization of gauge theories are perhaps appropriate here.
These topics are generally considered to be the more formal
aspects of gauge theories, and many of the papers are fairly
difficult to understand. Thus forewarned, the readers should
not feel discouraged if they find the papers in these sections
rough going. Also, the papers on these topics that are included
here are only representative fragments of the existing literature 1979 NOBEL LECTURES
- many other relevant and influential papers have been dropped
from our preliminary list at the suggestions of many physicists
we consulted. It is likely that these additional papers, along
with papers on the gauge theory of the strong interactions,
grand unified theories and related topics, will appear in a sequel
to this volume.
We would like to thank Professors C. N. Yang, A. Salam,
M. Jacob and A. Zee for their interests and suggestions, and
Professor R. N. Mohapatra, consulting editor of this volume,
for his many contributions. Dr. K. K. Phua initiated this project
and provided much encouragement and the necessary pressure
during the final stages of the compilation. We are also indebted
to the various journals and the Nobel Foundation for theh
permissions to reproduce the papers in this volume.
C. H. LAI
November 1980
1
Conceptual foundations of t he unified theory of w e ak a nd
electromagnetic interactions'"^
Steven Weinberg
Lyman Laboratory of Physics, Harvard University
and Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 U.S.A.
Our job in physics is to see things simply, to under apparently governed by quite different symmetries.
stand a great many complicated phenomena in a unified Matters became yet more confusing with the recognition
way, in terms of a few simple principles. At times, in the early 1960s of a symmetry group—the "eight
our efforts are illuminated by a brilliant experiment, fold way"—which is not even an exact symmetry of the
such as the 1973 discovery of neutral current neutrino strong interactions.''
reactions. But even in the dark times between experi These are all "global" symmetries, for which the
mental breakthroughs, there always continues a steady symmetry transformations do not depend on position in
evolution of theoretical ideas, leading almost imper space and time. It had been recognized^ in the 1920s
ceptibly to changes in previous beliefs. In this talk, I that quantum electrodynamics has another symmetry
want to discuss the development of two lines of thought of a far more powerful kind, a "local" symmetry under
in theoretical physics. One of them is the slow growth transformations in which the electron field suffers a
in our understanding of symmetry, and in particular, phase change that can vary freely from point to point
broken or hidden symmetry. The other is the old in space-time, and the electromagnetic vector potential
struggle to come to terms with the infinities in quantum undergoes a corresponding gauge transformation. To
field theories. To a remarkable degree, our present day this would be called aU(l) gauge symmetry, be
cause a simple phase change can be thought of as multi
detailed theories of elementary particle interactions
plication by a Ix 1 unitary matrix. The extension to
can be understood deductively, as consequences of sym
more complicated groups was made by Yang and Mills*
metry principles and of a principle of renormalizability
in 1954 in a seminal paper in which they showed how to
which is invoked to deal with the infinities. I will also
construct an SU(2) gauge theory of strong interactions.
briefly describe how the convergence of these lines of
(The name "SU(2)" means that the group of symmetry
thought led to my own work on the unification of weak
transformations consists of 2x2 unitary matrices that
and electromagnetic interactions. For the most part, are "special," in that they have determinant unity.)
my talk will center on my own gradual education in But here again it seemed that the symmetry, if real at
these matters, because that is one subject on which 1 all, would have to be approximate, because at least
can speak with some confidence. With rather less con on a naive level gauge invariance requires that vector
fidence, I will also try to look ahead, and suggest what bosons like the photon would have to be massless, and
role these lines of thought may play in the physics of it seemed obvious that the strong interactions are not
the future. mediated by massless particles. The old question re
Symmetry principles made their appearance in twen mained: if symmetry principles are an expression of
tieth century physics in 1905 with Einstein's identifica the simplicity of nature at its deepest level, then how
tion of the invariance group of space and time. With can there be such a thing as an approximate symmetry?
this as a precedent, symmetries took on a character Is nature only approximately simple?
in physicists' minds as a priori principles of universal
validity, expressions of the simplicity of nature at its Sometime in 1960 or early 1961, I learned of an idea
deepest level. So it was painfully difficult in the 1930s which had originated earlier in solid state physics and
to realize that there are internal symmetries, such as had been brought into particle physics by those like
isospin conservation,^ having nothing to do with space Heisenberg, Nambu, and Goldstone, who had worked in
and time, symmetries which are far from self-evident, both areas. It was the idea of "broken symmetry,"
and that only govern what are now called the strong in that the Hamiltonian and commutation relations of a
teractions. The 1950s saw the discovery of another quantum theory could possess an exact symmetry, and
internal symmetry—the conservation of strange that the physical states might nevertheless not provide
ness^—which is not obeyed by the weak interactions, neat representations of the symmetry. In particular,
and even one of the supposedly sacred symmetries of a symmetry of the Hamiltonian might turn out to be not
space-time—parity—was also found to be violated by a symmetry of the vacuum.
weak interactions.^ Instead of moving toward unity, As theorists sometimes do, I fell in love with this
physicists were learning that different interactions are idea. But as often happens with love affairs, at first 1
was rather confused about its implications. I thought
(as it turned out, wrongly) that the approximate sym
*Thts lecture was delivered December 8, 1979, on the occa metries—parity, isospin, strangeness, the eightfold
sion pf the presentation of the 1979 Nobel Prizes in Physics. way—might really be exact a priori symmetry princi
ples, and that the observed violations of these sym
metries might somehow be brought about by spontaneous
symmetry breaking. It was therefore rather disturbing
1980 The Nobet Foundation
2
Steven Weinberg: Unified theory of weak and electromagnetic interactions Steven Weinberg: Unified theory of weak and electromagnetic interactions
for me to hear of a result of Goldstone,' that in at least for low energy pionic reactions. In this approach, the ies no coupling constants can have the dimensions of necessary to insert a common p and/41 mass term in
one simple case the spontaneous breakdown of a con Adler-Weisberger sum rule is obtained by using the negative powers of mass. But every time we add a field the Lagrangian, and the spontaneous breakdown of the
tinuous symmetry like isospin would necessarily entail predicted pion nucleon scattering lengths in conjunction or a space-time derivative to an interaction, we reduce SU(2)x SU(2) symmetry would then split the p andAl
the existence of a massless spin zero particle—what with a well-known sum rule,^^ which years earlier had the dimensionality of the associated coupling constant. by something like the Higgs mechanism, but since the
would today be called a "Goldstone boson." It seemed been derived from the dispersion relations for pion- So only a few simple types of interaction can be re theory would not be gauge invariant the pions would re
obvious that there could not exist any new type of mass nucleon scattering. normalizable.) In particular, the existing Fermi theory main as physical Goldstone bosons. This theory gave
less particle of this sort which would not already have In these calculations one is really using not only the of weak interactions clearly was not renormalizable. an intriguing result, that the Al/p mass ratio should be
been discovered. fact that the strong interactions have a spontaneously (The Fermi coupling constant has the dimensions of ^/2, and in trying to understand this result without re
I had long discussions of this problem with Goldstone broken approximate SU(2)xSU(2) symmetry, but also [mass]"^.) The sense of discouragement about quantum lying on perturbation theory, I discovered certain sum
at Madison in the summer of 1961, and then with Salam that the currents of this symmetry group are, up to an field theory persisted into the 1950s and 1960s. rules, the "spectral function sum rules,"^^ which turned
while I was his guest at Impei-ial College in 1961-62. overall constant, to be identified with the vector and I learned about renormalization theory as a graduate out to have a variety of other uses. But the SU(2) x SU(2)
The three of us soon were able to show that Goldstone axial vector currents of beta decay. (With this assump student, mostly by reading Dyson's papers.From the theory was not gauge invariant, and hence it could not
bosons must in fact occur whenever a symmetry like tion gA/gv gets into the picture through the Goldberger- beginning it seemed to me to be a wonderful thing that be renormalizable,^'* so I was not too enthusiastic about
isospin or strangeness is spontaneously broken, and Treiman relation," which gives gA/gv in terms of the very few quantum field theories are renormalizable. it." Of course, if I did not insert the P--41 mass term
that their masses then remain zero to all orders of pion decay constant and the pionnucleoncoupling.) Here, Limitations of this sort are, after all, what we most in the Lagrangian, then the theory would be gauge in
perturbation theory. I remember being so discouraged in this relation between the currents of the symmetries want; not mathematical methods which can make sense variant and renormalizable, and the Al would be mas
by these zero masses that when we wrote our joint of the strong interactions and the physical currents of out of an infinite variety of physically irrelevant theor sive. But then there would be no pions and the P mes
paper on the subject,^ I added an epigraph to the paper beta decay, there was a tantalizing hint of a deep con ies, but methods wliich carry constraints, because ons would be massless, in obvious contradiction (to
to underscore the futility of supposing that anything nection between the weak interactions and the strong in these constraints may point the way toward the one true say the least) with observation.
sctoautlde: beit ewxpasla Lineeadr 'sin rteetromrst toof aC onrodneilniav, ar"iNaontt hivnag cuwuiml l tsetroaodc tifoonrs. a lmBoutst tha is dceocnadnee. ction was not really under ftahcet otrhy.a t qInua pnatrumt iceulelacrt,r oId wynaasm viecs ry ciomulpdre ssined a bsyen steh e be to Atm ys oomfef icpeo iantt MinIT ,t heit f aolcl cuofr r1e9d6 7t, o Im eth itnhk atw hI ihle add rbiveeinn g
come of nothing: speak again." Of course, The Physi I spent the years 1965-67 happily developing the im derived from symmetry principles and the constraint applyii^ the right ideas to the wrong problem. It is not
cal Review protected the purity of the physics litera plications of spontaneous symmetry breaking for the of renormalizability; the only Lorentz invariant and the p meson that is massless: it is the photon. And its
ture, and removed the quote. Considering the future of strong interactions.^^ It was this work that led to my gauge invariant renormalizable Lagrangian for photons partner is not theAl, but the massive intermediate
the noninvariant vacuum in theoretical physics, it was 1967 paper on weak and electromagnetic unification. and electrons is precisely the original Dirac Langran- bosons,'which since the time of Yukawa had been sus
just as well. But before I come to that I have to go back in history gian of QED. Of course, that is not the way Dirac pected to be the mediators of the weak interactions.
There was actually an exception to this proof, pointed and pick up one other line of thought, having to do with came to his theory. He had the benefit of the informa The weak and electromagnetic interactions could then
out soon afterwards by Higgs, Kibble, and others.^ the problem of infinities in quantum field theory. tion gleaned in centuries of experimentation on electro- be described^^ in a unified way in terms of an exact but
They showed that if the broken symmetry is a local, I believe that it was Oppenheimer and Waller in 1930^^ magnetism, and in order to fix the final form of his spontaneously broken gauge symmetry. [Of course,
gauge symmetry, like electromagnetic gauge invariance, who independently first noted that quantum field theory theory he relied on ideas of simplicity (specifically, not necessarily SU(2)x SU(2).] And this theory would
then although the Goldstone bosons exist formally, and when pushed beyond the lowest approximation yields on what is sometimes called minimal electromagnetic be renormalizable like quantum electrodynamics be
are in some sense real, they can be eliminated by a ultraviolet divergent results for radiative self-ener coupling). But we have to look ahead, to try to make cause it is gauge invariant like quantum electrodynam
gauge transformation, so that they do not appear as gies. Professor Waller told me last night that when he theories of phenomena which have not been so well ics.
physical particles. The missing Goldstone bosons described this result to Pauli, Pauli did not believe it. studied experimentally, and we may not be able to trust
appear instead as helicity zero states of the vector It must have seemed that these infinities would be a purely formal ideas of simplicity. I thought that re It was not difficult to develop a concrete model which
particles, which thereby acquire a mass. disaster for the quantum field theory that had just been normalizability might be the key criterion, which also embodied these ideas. I had little confidence then in my
ttttThhhrheI uies isod rt reloeiermlxiestnc ik ae cytpotaolfht h ia tptoaGhnh v oaet yalg tdsbeoi setfnctehs eon,w e rnee ab wtlleihbclmcy iooea cshmru opeesenh sgs uya fdsfrridrodicfeoee imdnans ldt yst nsh. i stae tewwaes hm daoeoed fvh eeutlane orcwpdt hoamnna eitbcncetoadh ul ati iinntn yg. e Sidtaqcnecoleudtmhvuaeeewrnprelaittndosn u,g apmgewte etdmiehrv e,ereeel nbssete. y acm at inaHrbndTdoeofe idiTuhntse yo ienq tmniaipnuboemrsa enotinr achbgtesgd lu) mea1iam d9,"anf , df i3lwteae0 elsadPnr da dasa t uD nhttsloidehyo eaosli r vone wyenas,d aer.1 "nrl9y, ( s2 e aI9 btta1 y-w 9lno3ed4f a0saF0 . mss det A fiaytosfnon uynom drn df aa innttd, h at libocmonfaino oetl niesartec yrit ,emr m ciupaoevoI sl arn eipwa bvcholiig eynutc yesclodn qiend ceuo sarnsalt tanlar h toyatahcnuui e omtrnot nhe rttivfsyehio erexne tal do torwbohtiuoauhiettrsute ldodto iarhf fiien tftedmoehsh r.erpe hieuo eeinssslnep UefyA io sunf ot Isi fo tttea do h warevpyie ,arlpln roe ioicbcekrebisxt msyeueptora l vulaoItiefk i nd az i tmnah d e uhuoctenhnolnae e nindcttcgdeatherrerrednyos o t tulnepraelI-anfx ettt deyc1U- itphen(r gao2mon nln)axedo - tlfpeUtdert yps (oipttclene or)es:-s,n o tls neay.a gp pclteltitoT hnine nthlu,gee nepr iraettootcahn ntareyais n,t o drhBne2 e tRset,o x,rw^2 g i,oes g ostmo ha hI talIenr -edt sh frowdttainae-icnehtcrhedsiat edend dre daa diecg wldelt hti-iotttn-h g y pe
In 1964 Adler and Weisberger^° independently derived all infinities disappear if one identifies the observed finite interactions is a good strategy. Filled with enthusiasm lepton. Breaking up U(2) into unimodular transforma
sum rules which gave the r3itio gji/gv oi axial-vector values of the electron mass and charge, not with the for renormalization theory, I wrote my Ph.D. thesis tions and phase transformations, one could say that the
to vector coupling constants in beta decay in terms of parameters m and e appearing in the Lagrangian, but under Sam Treiman in 1957 on the use of a limited group was SU(2)x U(l)x U(i). But then one of the U(l)'s
pion-nucleon cross sections. One way of looking at with the electron mass and charge that are calculated version of renormalizability to set constraints on the could be identified with ordinary lepton number; and
their calculation (perhaps the most common way at the from m and e, when one takes into account the fact that weak interactions,^" and a little later I worked out a since lepton number appears to be conserved and there
time) was as an analog to the old dipole sum rule in the electron and photon are always surrounded with rather tough little theorem^^ which completed the proof is no massless vector particle coupled to it, I decided
atomic physics: a complete set of hadronic states is clouds of virtual photons and electron-positron pairs." by Dyson" and Salam^' that ultraviolet divergences to exclude it from the group. This left the four-pa
inserted in the commutation relations of the axial vec Suddenly all sorts of calculations became possible, and really do cancel out to all orders in nominally re rameter group SU(2)x U(l). The spontaneous breakdown
tor currents. This is the approach memorialized in gave results in spectacular agreement with experi normalizable theories. But none of this seemed to help of SU(2)x U(l) to the U(l) of ordinary electromagnetic
the name of "current algebra."^' But there was another ment. with the important problem, of how to make a re gauge invariance would give masses to three of the four
way of looking at the Adler-Weisberger sum rule. One normalizable theory of weak interactions. vector gauge bosons: the charged bosons H^S and a
could suppose that the strong interactions have an ap But even after this success, opinions differed as to neutral boson that I called the Z°. The fourth boson
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4
Steven Weinberg: Unified theory of vveal< and electromagnetic interactions Steven Weinberg: Unified theory of weak and electromagnetic interactions
whose vacuum expectation values could give the elec gauge theories) by a paper of Ben Lee," and alter Lee's markable SLAC-Yale experiment*' last year, for the standing of symmetry principles. Once again, the con
tron a mass is a spin zero SU(2) doublet (/)°), so for paper 1 was ready to regard the renormalizabiUty of the electron-nucleon neutral currents as well. straints of gauge invariance and renormaUzability
simplicity 1 assumed that these were the only scalar unified theory as essentially proved. This is all very nice. But I must say that I would not proved enormously powerful. These constraints force
fields in the theory. The mass of the Z" was then deter By this time, many theoretical physicists were be have been too disturbed if it had turned out that the the Lagrangian to be so simple, that the strong inter
mined as about 80 GeV/sin2e. This fixed the strength coming convinced of the general approach that Salam correct theory was based on some other spontaneously actions in QCD must conserve strangeness, charge
of the neutral current weak interactions. Indeed, just and 1 had adopted: that is, the weak and electromagnetic broken gauge group, with very different neutral cur conjugation, and (apart from problems" having to do
as in QED, once one decides on the menu of fields in interactions are governed by some group of exact local rents. One possibility was a clever SU(2) theory pro with instantons) parity. One does not have to assume
(he theory, all details of the theory are completely de gauge symmetries; this group is spontaneously broken posed in 1972 by Georgi and Glashow,'*' which has no these symmetries as a priori principles; there is
termined by symmetry principles and renormalizability, to U(l), giving mass to all the vector bosons except the neutral currents at all. The important thing to me was simply no way that the Lagrangian can be complicated
with just a few free parameters: the lepton charge and photon; and the theory is renormalizable. What was the idea of an exact spontaneously broken gauge sym enough to violate them. With one additional assump
masses, the Fermi coupling constant of beta decay, the not so clear was that our specific simple model was the metry, which connects the weak and electromagnetic tion, that the u and d quarks have relatively small
mixing angle 9, and the mass of the scalar particle. one chosen by nature. That, of course, was a matter for interactions, and allows these interactions to be re masses, the strong interactions must also satisfy the
(It was of crucial importance to impose the constraint experiment to decide. normalizable. Of this I was convinced, if only because approximate SU(2)xSU(2) symmetry of current alge
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The next question now was renormalizability. The Wentzel, and again in 1958 by Bludman and Leite- to what otherwise would have been a serious problem, interactions also described by a gauge theory, the weak
Feynman rules for Yang-Mills theories with unbroken Lopes. Attempts at a unified weak and electromagnetic that of neutral strangeness changing currents. I leave currents are necessarily just the currents associated
gauge symmetries had been worked out'"' by deWitt, theory had been made" by Glashow and Salam and Ward this topic for Professor Glashow's talk. The other with these strong interaction symmetries. In other
Faddeev, and Popov and others, and it was known that in the early 1960s, and these had neutral currents with theoretical development has to do specifically with the words,.pretty much the whole pattern of approximate
such theories are renormalizable. But in 19611 did many of the features that Salam and 1 encountered in strong interactions, but it will take us back to one of symmetries of strong, weak, and electromagnetic
not know how to prove that this renormalizability was developing the 1967-68 theory. But since one of the the themes of my talk, the theme of symmetry. interactions that puzzled us so much in the 1950s and
not spoiled by the spontaneous symmetry breaking. 1 predictions of our theory was a value for the mass of In 1973, Politzer and Gross and Wilczek discovered" 1960s now stands explained as a simple consequence
worked on the problem on and off for several years, the Z°, it made a definite prediction of the strength of a remarkable property of Yang-Mills theories which of strong, weak, and electromagnetic gauge invariance,
partly in collaboration with students," but I made little the neutral currents. More important, now we had a they called "asymptotic freedom"—the effective coupling plus renormalizability. Internal symmetry is now at
progress. With hindsight, my main difficulty was that comprehensive quantum field theory of the weak and constant*' decreases to zero as the characteristic en the point where space-time symmetry was in Einstein's
in quantizing the vector fields 1 adopted a gauge now electromagnetic interactions that was physically and ergy of a process goes to infinity. It seemed that this day. All the approximate internal symmetries are ex
known as the unltarity gauge'": this gauge has several mathematically satisfactory in the same sense as quan might explain the experimental fact that the nucleon be plained dynamically. On a fundamental level, there are
wonderful advantages, it exhibits the true particle spec tum electrodynamics—a theory that treated photons and haves in high energy deep inelastic electron scattering no approximate or partial symmetries; there are only
trum of the theory, but it has the disadvantage of mak intermediate vector bosons on the same footing, that as if it consists of essentially free quarks.*" But there exact symmetries which govern all interactions.
ing renormalizability totally obscure. was based on an exact symmetry principle, and that al was a problem. In order to give masses to the vector
Finally, in 1971 't Hooft" showed in a beautiful paper lowed one to carry calculations to any desired degree bosons in a gauge theory of strong interactions one 1 now want to look ahead a bit, and comment on the
how the problem could be solved. He invented a gauge, of accuracy. To test this theory, it had now become would want to include strongly interacting scalar fields, possible future development of the ideas of symmetry
like the "Feynman gauge" in QED, in which the Feyn urgent to settle the question of the existence of the neu and these would generally destroy asymptotic freedom. and renormalizability.
man rules manifestly lead to only a finite number of tral currents. Another difficulty, one that particularly bothered me, We are still confronted with the question whether the
tigbvospttMttsocsfyofhhpieiy or a e zoaee npousnpmentcroLtdevlheser ds hi eroe adoofe ti,eiw oiocte mc e rb o nssotfoae e,feba elhtbn yn cn e lhwgevgusdefac aoaabhital.tni)b ayorurltiun t ustturycagZ lggh.she oase uiyere eiT,.ern v snntis bi(tih ehsiinn eoTnsBeoagoad-vlt hi eu eJpnanspti cga si euarrfsnc rta dhi moishtehutnogaioUweieasfgh,ivlnn se te teo euc aihearbwsrRi el oapsvagnt d Lolcra pireenvusdsaoec dlans aaedgnka vucfr settebruse,ieidpuoivf.taosrays ieber inl nfnn 'ba serattgict ia eilsewia tItdneqstdnHya i,h rhnpdtuo wismoernee even osoy bScamneifsrsiittotyrut ee fn sfotlgg iny et canw tar ae lstre yhfaolnino,c"gettsca d co uaah olceht n euslmoseyh Va pofbgntapove aehe eess,loylriLgtcsae ts haae atetmiqa meuitgtstsso nusaodgshro e aefane'ya a*tr .ti t tnh rn e y e rys atomifncnrtFpe1onf orueee xo 9oapuranluurLps6ltfnorn rttt ysaae7dshoerreieik tc r -cedt aibnnw6pZliu t ani8is ^mne erctoilt-a nosoycrtreip a e pe ut ue tnlnr1dhihi lnbprpteoc9testya erpr erct7m s,vo e plheeaee1e.r"pi rhn,t rtsya xter t dieosyho ab,iIo xdpsc p anowrtT prgcsr eeur oeedaoeocisednhincnlfatclpdr sca eteesen0 ,eieerdridsr w. g mr .s uvru 1lohese5ieple,tfwcd soi eepn dl d c0h utheteto. iQlrt1 a hstcth.ro"qsh02 e eabh ±uo.u e odw2 twiiuS mc u5etmaoaeee0te,o ,tnu r l . prerefb0tdea osl csr6rnehsut twoesett eu rwditsiosrco dai een orInspyys nt p irfo i et shkeaoopwtnacho neniutrh fredarn deasenuto titdsgspih ,dn.th ne g a te geurt etrao hr alcvalnrPa icoettet oolenerehwdnigtwri osu.xye hiae, nt r t vpaarrthooei eo fgrafenIfofn lr a deeh t duoaic ai sftc anm umm ovdsueg euatohuerun. n h ln oedunt e a l wqiwoiaamsrmoosocnffrnuclcnoea a h edu etstytaan m vtttoe c"irlsehirohhcrg tqgatyker eeohonaeulrr s stou atcutsvm.u taslr,htlt*oodaoata er'di oelo nbrt okf rei (si,nrosrto nltoid ahs,nreAa" aon hgn rnaat mr ,eatd aelt tsg feeaasaelu os ho rowsinreoortn"wr vmwec ifyaihm ccinyeaff ieeu. e eoo oldimun*slldn g'llew rea n dpiaaobe wpid radoatrssArltt eshietiiaetses roh"tnso nwhmcthlt k ensdsevteih seoet ue1itrene shnrrn sno/ omiycsnof1t,tct nteo a im3rn lrfsyotliaq cnoro7ge o hagc,a uwpnfhlae ysg bt a a ne tcsoswodh riroihaini slknnsnaeoikntGa tepgsrottth aty or skrcr eensees g trdsoilor ( rteahtyniua,asrgagaesswhis pcnocl et n n dotlugtnvadaieo iiauio ,eg snfnn no n lngsgctnlnddocys d1 esdtn rteio9 sro o lgc w rt7iWicea atna3ianhnigs ca nthu tie tthtreelblgitgrodeetr oaiecfo er or nnot z st n diamtbheoohsneceueyeetokenax cytsf)c rs ce sgip fr ,m fcneenile egsuclat aeadehtsrist rsn e e a in ct Xszfdmbbih"bedafot tfocou exioeroo euugmarcrixesm(shneoaa nscltloato t d ) ae rnska,rn fra smylste d iaaes ainebhtwatosgte. wper"esm7seh hwx aot1 enhsitte ir ,rur- nwe rnu i uottnalrAdre htend ion, ae rnefcaansid g nattgd"rfltokmt r shaleftmir hsl lcetleeyy eoidtoena s eoahrn thrt n detgeee gtdhe a Gcteinol e reatesaolee stburef cerscemtlmaet aeiVico awn wy cepn.yatw liopvtn tigratnarl.ueoeiyn thoe,rd r gTocl esa dwati h nth drTrskhb"eou sihyeteresa"snhalH. neicksa eo ern idabpvenp"wwrcegyrooettgnso e ogeiiIescna ssdfx tnb w hoosus ptg rttbnoitm,igor hroMteaabhbuos .ap ohsaelslltesddeey evosso o cx atsiyVsnespaidr sp,afismetssrOloty"t os-arn aro mnnemeawrtee t bssg,usaeett pe"as ha. h d"ihhtdptenvbntoeeeo ofre a hydluo - yetrb eaw GlrsinQdtcTtoi pcieon e atC ccoShnlhdslvflelndUhDtspe ieroeoarwts,sn ai( benrgsa t oHsy 2eneb hno )p u ic aenulrgedeotno , fog sud s,
I have to admit that when I first saw't Hooft's paper As everyone knows, neutral currents were finally lier work of several authors*'), and an SU(3) gauge be felt by new families of fermions, and would give
in 1971, 1 was not convinced that he had found the way discovered" in 1973. There followed years of careful group, one then had a specific theory of strong inter these fermions masses of the order of several hundred
to prove renormalizability. The trouble was not with experimental study on the detailed properties of the actions, the theory now generally known as quantum GeV. We shall see.
't Hooft, but with me: I was simply not familiar enough neutral currents. It would take me too far from my chromodynamics.
with the path integral formalism on which't Hooft's subject to survey these experiments," so I will just say Of the four (now three) types of interactions, only
work was based, and I wanted to see a derivation of the that they have confirmed the 1967-68 theory with steadi Experimeits since then have increasingly confirmed gravity has resisted incorporation into a renormalizable
Feynman rules in't Hooft's gauge from canonical quan ly improving precision for neutrino-nucleon and neutrino- QCD as the correct theory of strong interactions. What quantum field theory. This may just mean that we are
tization. That was soon supplied (for a limited class of electron neutral current reactions, and since the re- concerns me here, though, is its impact on our under not being clever enough in our mathematical treatment
6
Steven Weinberg: Unified theory of weak and electromagnetic interactions
Steven Weinberg: Unified theory of weak and electromagnetic interactions
of general relativity. But there is another possibility Thus, the fact that ordinary matter seems pretty sta from the spontaneous breakdown of the grand unified of the theory?
that seems to me quite plausible. The constant of ble, that proton decay has not been seen, should not gauge group. There is nothing impossible in this, I think the answer must lie in the fact that the quan
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which superheavy degrees of freedom do not explicitly baryon nonconserving processes have actually oc of the grand unified gauge group, then as I have al to infinity. However, to require this behavior generally
appear, but the coupling parameters implicitly repre curred. If effects of a tiny nonconservation of baryon or ready mentioned, there must be extra strong forces imposes so many constraints on the couplings that there
sent sums over these hidden degrees of freedom. lepton number such as proton decay or neutrino masses to bind the composite Goldstone and Higgs bosons are only a finite number of free parameters left^^—just
are discovered experimentally, we will then be left as for theories that are renormalizable in the usual
To see if this makes sense, let us suppose it is true, that are associated with the spontaneous breakdown of
and ask what kinds of interactions we would expect on with gauge symmetries as the only true internal sym SU(2)x U(l). Such forces can occur rather nahirally in sense. Thus, one way or another, I think that quantum
this basis to find at ordinary energy. By "integrating metries of nature, a conclusion that I would regard as grand unified theories. To take one example, suppose field theory is going to go on being very stubborn, re
out" the superhigh energy degrees of freedom in a most satisfactory. that the grand gauge group breaks, not into SU(3) fusing to allow us to describe all but a small number of
fundamental theory, we generally encounter a very The idea of a new scale of superheavy masses has xsu(2)xu(l), but into SU(4)xsU(3)xSU(2)xU(l). Since possible worlds, among which, we hope, is ours.
complicated effective field theory—so complicated, in arisen in another way.^ If any sort of "grand unifica SU(4) is a bigger group than SU(3), its coupling constant I suppose that I tend to be optimistic about the future
fact, that it contains all interactions allowed by sym tion" of strong and electroweak gauge couplings is rises with decreasing energy more rapidly than the of physics. And nothing makes me more optimistic than
metry principles. But where dimensional analysis to be possible, then one would expect all of the SU{3) QCD coupling, so the SU(4) force becomes strong at a the discovery of broken symmetries. In the seventh
tells us that a coupling constant is a certain power of and SU{2)x U(l) gauge coupling constants to be of com much higher energy than the few hundred MeV at which book of The Republic, Plato describes prisoners who
some mass, that mass is likely to be a typical super parable magnihide. (In particular, if SU{3) and SU(2) the QCD force becomes strong. Ordinary quarks and are chained in a cave and can see only shadows that
heavy mass, such as 10" GeV. The infinite variety of X u(l) are subgroups of a larger simple group, then leptons would be neutral under SU(4), so they would things outside cast on the cave wall. When released
nonrenormalizable interactions in the effective theory the ratios of the squared couplings are fixed as rational not feel this force, but other fermions might carry from the cave at first their eyes hurt, and for a while
have coupling constants with the dimensionality of nega numbers of order unity.^"0 But this appears in con SU(4) quantum numbers, and so get rather large masses. they think that the shadows they saw in the cave are
tive powers of mass, so their effects are suppressed tradiction with the obvious fact that the strong inter One can even imagine a sequence of increasingly large more real than the objects they now see. But eventually
at ordinary energies by powers of energy divided by actions are stronger than the weak and electromagnetic subgroups of the grand gauge group, which would fill their vision clears, and they can understand how beauti
superheavy masses. Thus the only interactions that we interactions. In 1974 Georgi, Quinn, and I suggested in the vast energy range up to 10" or 10" GeV with ful the real world is. We are in such a cave, i m
can detect at ordinary energies are those that are re that the grand unification scale, at which the couplings particle masses that are produced by these successively prisoned by the limitations on the sorts of experiments
normalizable in the usual sense, plus any nonrenorma are all comparable, is at an enormous energy, and that strong interactions. we can do. In particular, we can study matter only at
lizable interactions that produce effects which, although the reason that the strong coupling is so much larger relatively low temperatures, where symmetries are
tiny, are somehow exotic enough to be seen. than the electroweak couplings at ordinary energies is If there are elementary scalars whose vacuum ex likely to be spontaneously broken, so that nature does
One way that a very weak interaction could be de that QCD is asymptotically free, so that its effective pectation values are responsible for the masses of not appear very simple or unified. We have not been
tected is for it to be coherent and of long range, so that coupling constant rises slowly as the energy drops from ordinary quarks and leptons, then these masses can be able to get out of this cave, but by looking long and hard
it can add up and have macroscopic effects. It has been the grand unification scale to ordinary values. The affected in order a by radiative corrections involving at the shadows on the cave wall, we can at least make
shown^'* that the only particles which could produce such change of the strong couplings is very slow (like the superheavy vector bosons of the grand gauge group, out the shapes of symmetries, which though broken,
forces are massless particles of spin 0, 1, or 2. And 1/Vln E) so the grand unification scale must be enor and it will probably be impossible to explain the value are exact principles governing all phenomena, expres
furthermore, Lorentz invariance alone is enough to mous. We found that for a fairly large class of theories of quantities like rrig/m^ without a complete grand uni sions of the beauty of the world outside.
show that the long-range interactions of any particle the grand unification scale comes out to be in the neigh fied theory. On the other hand, if there are no such It has only been possible here to give references to a
of mass zero and spin 2 must be governed by general borhood of 10" GeV, an energy not all that different elementary scalars, then almost all the details of the very small part of the literature on the subjects dis
relativity.Thus from this point of view we should not from the Planck energy of 10" GeV. The nucleon life grand unified theory are forgotten by the effective field cussed in this talk. Additional references can be found
time is very difficult to estimate accurately, but we theory that describes physics at ordinary energies, and
be too surprised that gravitation is the only interaction in the following reviews: E. S. Abers and B. W. Lee,
gave a representative value of 10^^ years, which may it ought to be possible to calculate quark and lepton
discovered so far that does not seem to be described by "Gauge Theories" (Phys. Rep. C 9, No. 1, 1973);
be accessible experimentally in a few years. (These masses purely in terms of processes at accessible en
a renormalizable field theory—it is almost the only W. Marciano andH. Pagels, "Quantum Chromodynamics"
estimates have been improved in more detailed calcu ergies. Unfortunately, no one so far has been able to
superweak interaction that could have been detected. lations by several authors.)^ We also calculated a see how in this way anything resembling the observed (Phys. Rep. C 36, No. 3, 1978); J. C. Taylor, Gauge
And we should not be surprised to find that gravity is value for the mixing parameter sin^e of about 0.2, not pattern of masses could arise.'"' Theories of Weak Interactions (Cambridge University,
well described by general relativity at macroscopic far from the present experimental value^° of 0.23 ±0.01. 1976).
scales, even if we do not think that general relativity It will be an important task for future experiments on Putting aside all these uncertainties, suppose that
applies at 10" GeV. neutral currents to improve the precision with which there is a truly fundamental theory, characterized by
Nonrenormalizable effective interactions may also be sin^e is known, to see if it really agrees with this pre an energy scale of order 10" to 10^^ GeV, at which
detected if they violate otherwise exact conservation diction. strong, electroweak, and gravitational interactions are
all united. It might be a conventional renormalizable
laws. The leading candidates for violation are baryon
quantum field theory, but at the moment, if we include
and lepton conservation. It is a remarkable consequence In a grand unified theory, in order for elementary
gravity, we do not see how this is possible. (I leave the
of the SU(3) and SU(2)x U(l) gauge symmetries of scalar particles to be available to produce the spon
topic of supersymmetry and supergravity for Professor
strong, weak, and electromagnetic interactions, that taneous breakdown of the electroweak gauge symmetry
Salam's talk.) But if it is not renormalizable, what
all renormalizable interactions among known particles at a few hundred GeV, it is necessary for
then determines the infinite set of coupling constants
automatically conserve baryon and lepton number. such particles to escape getting superlarge masses
that are needed to absorb all the ultraviolet divergences
8 9
37. Weinberg. S. Phyi. Rev. 5. 1412 (1972).
38. C^indy. D. C. et. al., Phys. Utt. 31B, 478 (1970).
39. The Fust published discovery of neutral currents was al the Gargamelle Bubble Chamber G a u ge unification of fundamental forces'^
at CERN: Haserl. F, J. et. al.. Phys. Utt, 46B, 121. 138 (1973). Also sec Musset. P. Jour,
de Physique 11/12 T34 (1973). Muonless events were seen at about the same time by the Abdus Salam
HPWF group at Fermilab, but when publication of their paper was delayed, they took the
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(7A14c99a, 4d,8 7);S5 c97i ,5 (.31 769.54 194 )5(;2 1 89(041.9 9)54; 1470);6 ,(T 17o99m500o n)(;1a 9gS4ac,9 h)Sw;. i5Pn2rg,oe gr6,r 6. JT4. h,P9eh1oy4rs. . (P1Rh9ey5vi1.. )(;J a97p3/a.. n 7)114 36 1 (.1 (219795 43(81);)9;4 P67r)4o;. c K. 1No4ba3al9., 52. Wdkiifenfiden,r beeLnr.t gP ,c hoSyns.. t reRexfet. v .b5y1 D.W T2e0hin,e b2pe6or sg1 .s 9i Sb.(i 1lPi9thy7y 9os.)f .R pesev.u dUot-tG.o ld2s9t.o n1e6 9b8o s(o1n9s7 w2)a.s originally noted in a "1T93h7e Nidoebael liLsme cwthuirceh. pSepremaekaintged ofh Aisl fcrheda rNaocbteerl, lehde hsima id: Acofguhnatrniiesst ano,f tbheut E aalssot , frliomke dSeyvreilao, pEingg yplat, nIdsran of atnhde West
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276 (1948); Koba. Z. and Tomonaga. S. ibid 3. 290 (1948). Suiskind, Lref. 51. as a whole, as individual scientists. ... The Swedish were obstacles to this international scientific concourse,
18. T(fi6he)le dr 1e9t h3he6ao,d r eiesbsp eeeicnni atlhelyais r plwi.e ar 3y,4s u agbngyde s pWtpioe.in ss5 i-kc6oh;pa ftK. rVian. mfFme. riKtt.i oeiHn .g c. o(Duuanldnpiuk b. lbiVseihd e.e dlS)i.me l,i nMataeld. -Ffyroi.m M eqdud.ant u1m5 5545.. aWWndee iinnFbbieeerrldgg ,, STS. h.Pe Pohrhyyys, .s . ReUedvt..t . b 1y93.5 3D. 5eB7se1 r(0,1 49S96. a4(1n);d9 6PF4ho)y,r sd. , RK.e (vP.rBen/Jti5c.e -mHa U,(19 651)9; 65)L,e cpt.u r9e8s 8;i na ndP raerft.ic l5es4 . ptheroopulegh utnhdeer m tehdei ulme adoef rtshheip R oofy tal heAc Raodyeaml yF aomfi lyS cainedn ces fweirthe nt anp aerctson oomf tich ea wnd orinldt. ellMecent ulali ked iMspicahriateyl betthew eSecno t doirf
19. Dyson. F. i. Phys. Rev. 75. 486, 1736 (1949). The program of deriving general relativity from quantum mechanics and special relativity have made Nobel Prizes one of the chief causes of the Henrik Harpestraeng were singularities. They did not
2201.. WWeeiinnbbeerrgg,, SS.. PPhhyyss.. RReevv.. 110168.. 813380 1( 1(916905)7.) . twhaast csoimmiplalre tiedde asb wye Breo udlewvaerloe.p edD .b ya nFd eDynesmera,n , SR.. Ainn un.n pPuhbylsi.s h8e9d. le1c7t3u r(es1 9a7l 5C)a. l.I Tuencdhe. rstand growth of the prestige of science in the eyes of the orwenp rceosuenntt raineys . flWouirthis hainlgl t hesc hboesot lsw iollf rine stehaer cwh orinld tthheeiri r
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57. An example of a simple gauge group for weak and electromagnetic interactions (for- sincerest thanks to them as well as to him."
2243.. WFoeri ntbhee rng,o Sn.- rPehnyori. mRaelvi.z aUbtilt.ity 1 8o,f 5th07eo (r1ie9i 6w7)i.t h intrinsically broken gauge lymmetriet, see wnuhmicbhe r sionf* es=pe-ic)i fiwc asm ogdiveelns obfy wSe.a Wk, eienlebcetrrgo, mPahgynse. tiRc, Eav.nd D s5t.r o1ng9 6i2n t(e1r9ac7t2io).n s TTbiaesreed ar eo na I am sure I am echoing my colleagues' feelings as vAta lulee asotf otrnae ionf ihng isth emma sfteorrs acdovuannsceedl ed scyieonutngi fic Mircehsaeela rch.
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25. T(2N18hu,9 ics6l 5.w8 2)oP9 ;rh kfy(l 12sw.9/a, 6 s2 132b).8r ;8i 3e Sf9(al19yl 9 ar7(me10,p9 )oA;6 r.1 Bt)ePo;dh u Kylinwsa . amrRreefee,ef vruD.ec.n hc1Aie,2 nS7n ..,. 2PO33h3,' Ry1fs ao.( io1(fNte9n.a 6or2Ytte)a.;) i g7V h. 5,e (l5Lt,.m a1an4nd, 0 SM(1a. 9lNa7mu0c,) l..A .P Nhyusc.l. fPlh7,y s6. 37 PA((11anr99nt77i.c 94le))Ps;; GhGyausen.ro dsre 9gFy3i,,i. e lFdH,1s 9.R 3aa( Anmd(m 1oe9Gnr7dUi.5c iPa)h;n. o aGwIn,nde ostSrSigit.kiu ,i Ltvei H eo, fP. P hP.a yhnPsdy.h syiRNcs.esa ,vnU. ot1pUt9o.tBu7t.lf5oi) ts;,J 3 ,F2r.D i t.14z 73sV7c8.h ( , (P1H19h.9 y7a7s5n.4 )d); U; MG tGtui.ner okser8oyg2w.i B.sF k.. Hi,a 3.nP 9d. 2i n wfslohnu eernseac ei idso— nt inht ihs reem sgoprreeo ctwtthr u et ooft hNtahonebe plir'sne tsgtheeinge e dreoovfse isltyoc piaeinnngd ce .w iotsrN liodn. of Inw oroelsenp ectc lootfh . this cycle of scientific disparity, per
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3301.. ('Mt1 y9H 7wo1oo)fr,tk , aGnwd. i tNdh eustcchl.re iPbuhendyl sti.an r mitfyoli Jr,g e adu1eg6et7 a wil( 1aisn9 7Wr1ee)p.io nrbteedr g.i nS .W Pehinybs.e rRge, vS,. P hDy7s,. R10ev6.8 L (e1t9t.73). 27, 1688 Jbl.oe gyCp uEobRflNi sn hupecdrle epoinrn i ndNt,eu cctaloye abrh eaPs phbuyebseilnci ss;h deWids.ce uiMnsbsaeedcrhga ,c ienSk .,g epMna,ep reHarla ritnvear prmdrs ep prbaerypar tWiinoetni.n TbHehUre gT, pPSh-7e. n9Po/hAmy0es2.n 1oR,n eotv-o. otfh rsocuigehn cce,y clleisk.e tPheer hhiasptso ryI coaf na illll ucsivtrilaitze atthiois n,w ithhas a ng one scoe notun.r iesF roomf A6r0i0s tAoDtl te,o 6o5f0 EADu cisl itd,h eof A rCchhiinmesee dehsa, lf and
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Gross and R. Jackiw, Phys. Rev. D6. 477 (1972) and C, Bouchiat, J. Iliopoulos, and Ph. mass of order 10 GeV, The spontaneous symmetry breaking in models with zero bare left his'native glens to travel south to Toledo in ^ain. of Jabir, Khwarizmi, Razi, Masudi, Wafa, Biruni,
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© 1980 The Nobel Foundation