Concepts and Trends in Particle Physics: Proceedings of the XXV Int. Universitätswochen für Kernphysik, Schladming, Austria, February 19–27, 1986

332 Pages·1987·11.66 MB·English

by  M. Blau, W. Thirring, G. Landi (auth.), Professor Dr. Heimo Latal, Professor Dr. Heinrich Mitter (eds.)

Concepts and Trends in
Particle Physics
Concepts and Trends
in Particle Physics
Proceedings of the
XXV Int. Universitatswochen fur Kernphysik
Schladming, Austria, February 19-27,1986
Editors: H. Latal and H. Mitter
With 48 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Professor Dr. Heimo Latal
Professor Dr. Heinrich Mitter
Karl-Franzens-Universitat, Institut fOr Theoretische Physik, Universitatsplatz 5,
A-B01O Graz, Austria
ISBN-13 :978-3-642-71762-8 e-ISBN-13: 978-3-642-71760-4
001: 10.1007/978-3-642-71760-4
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© Springer-Verlag Berlin Heidelberg 1987
Softcover reprint of the hardcover 1st edition 1987
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2153/3150-543210
Preface
Twenty-five years of Schladming Winter School
1. The Start
Twenty-five years ago P. Urban had the idea of organizing a winter school
in the Austrian mountains. The very concept of a school was not new: to
bring physicists together in an environment which differs totally from the
daily world of institutes and laboratories, to contrast hard classroom work
in lectures by distinguished speakers with a relaxed atmosphere, to provide
opportunities for entering newly developing fields and exchanging ideas, all
this had already resulted in a few summer schools in southern Europe and
the US. The idea of combining physics with skiing rather than swimming
was, however, new. After some sampling by a few younger members of Ur
ban's group, Schladming was selected as an appropriate place. At that time
skiing was not very much developed here; there were few lifts, but a road to
Hochwurzen and a regular bus service opened at least one longer track. The
first meeting took place in a classroom of the local school, w here some 40
participants were squeezed into benches designed for children. In the next
year we moved into the dining hall of a small inn, which does not exist any
more (an attempt to serve beer during the lectures was stopped by the orga
nizing committee). Only in later years did we find a permanent home here
in the Stadtsaal. The name of the school (Kern physik = nuclear physics) is
reminiscent of its foundation: at that time particle physics was still part of
nuclear physics. Since Austrians stick to tradition, we have kept the name.
2. Skiing
The intimate mixture of snow and physics is a characteristic of our school.
The clean air of the mountains is a good refreshment between hard lectures
(and it may be amusing to watch your opponent in a violent scientific discus
sion landing in the snow next to you). We had ardent skiers: one of them (by
now a distinguished professor) went down all the way from Hauser Kaibling
on the third day he had ever spent on skis. Fortunately we had few accidents
at the school. Our relations to the local hospital are very good (the brother
of its medical director is a former student of Prof. Urban's, of course), but
we have not added very much to its record. Some broken legs, a broken finger
(due to bowling, not skiing!): this is not very much compared with the yearly
v
supply of 2 waggon loads of plaster consumed in Schladming's hospital. Let
us hope that our contribution remains that small also in the future!
3. The People
Professor Urban has organized 15 Schladming schools in a row. He was
(and still is) the heart of the whole business. He was able to attract excel
lent lecturers and select interesting topics. The fame of the school increased
rapidly, and so did the number of participants. Schladming became known
world-wide in the community of physicists long before it became famous for
world champions and world cup ski races.
From the long list of lecturers I can only mention a few names. Cunnar
Kiillen was present at the very first school. He hurt his hand on the first slope
that he went down on skis (straight down, of course; he was used to cross
country skiing). When the mayor of Schladming shook his hand, it turned
out to be broken. This did not prevent him from discussing physics at the
same evening with his hand in plaster. He returned to Schladming every year
until his tragic death in an airplane crash. Five of our lecturers have received
the Nobel prize so far: K. Wilson has been here twice, A. Salam, S. Clashow,
M. Cell-Mann, and J. Schwinger once (a sixth member of this group we just
missed today: C. Rubbia had already bought his flight ticket, when he was
called back for a CERN meeting). In saying "so far" I wanted to indicate
that the prize has been awarded to three of the five after they had lectured
here. According to our records a Schladming lecturer has a chance to win the
prize about nine years after coming here. It is, of course, our policy to have
enough "irons in the fire" for future prizes. In fact, the process usually starts
much earlier: quite a few physicists, who had been here as students, returned
as distinguished lecturers in later years. Apparently, snow is a stimulating
agent. Let us hope that this process continues.
4. Politics
In spite of physics being a totally international subject, we live, unfortu
nately, in a world consisting of borders. Borders between nations, creeds,
political and economic systems. It is an Austrian attitude that has helped
us to avoid any related trouble so far: If two Austrians discuss politics and
one expresses his opinion, the other one will express a contrary one. If you
expect a clash, you are wrong - the first one will just say, "This may also be
true". This kind of double truth is what we have learnt from our history. We
consider borders not as lines separating countries, but connecting them, as
bridges rather than ditches. So we have successfully tried, with our school,
to bridge the big borders on our small scale. This has worked out through
25 years now, irrespective of varying tensions between different countries and
systems. We are proud that we have always had participants from East and
West, North and South. Despite all differences in personal belief and opinion
it has never happened that political troubles have endangered the climate
VI
of our school. Let us hope that this climate remains unchanged also in the
future.
5. Ideas
Let me finally come to the ideas presented here. A school like this one
will never be free from what is fashionable in particle physics. Throughout
the years many ideas have been discussed here, which we would now call
momentary deviations from the general line of development. Quite a few
subjects were presented here, however, which turned out to be very impor
tant much later. Non-Abelian gauge theory (the SU(2) Yang-Mills-theory)
was discussed here at the very first school 25 years ago, supersymmetry two
years later. The meeting in 1965 brought the hardest scientific duel I have
ever seen: the issue was whether QED may be a finite theory: the opponents
were K. Johnson and G. Kiillen. The fight was so hard that even Bjorken was
not able to bridge the controversy despite his excellent summary, and Urban
needed all his specific Austrian personal abilities (and many liters of wine) to
bring the two opponents to one table at the end. - Static SU(6) properties
in the quark model were discussed at the same meeting. Spontaneous sym
metry breaking can be found on our list already in 1966, the first lecture on
differentiable manifolds was given in 1970 by an expert mathematician. This
is just a small selection from the earlier times. Problems, which might have
appeared to many participants as queer speculations at the time they were
presented here, turned out to be important issues and have accompanied us
until today. So one could find many roots of the subjects of this year's meet
ing already one or two decades ago. We shall see whether this will happen
also with subjects from later schools. Let us hope so.
Two aspects of our school should not be forgotten, because they are rather
specific:
One concerns the role of mathematics. It is traditional to have, at least
from time to time, lectures on the mathematical foundations of physics. Ev
ery once in a while mathematical physics may even be a major subject of the
school, even if this is usually a hard piece of bread to chew for people oriented
towards the phenomena. We should not forget, however, that physics owes
much of its strength to its mathematical foundation, and if mathematicians
teach us that there is progress in their field, we should learn the lesson.
The other aspect is experiment. Although the main emphasis of the school
is on theory, we have always asked experimentalists to lecture on their results.
Sometimes we had to stand a bombardment with drawings of hardware and
error bars, but more than once the experimental lectures turned out to be the
best of the whole school. Originally these lectures were chosen with the intent
to bring theorists from the thin air of their speculations down to the solid
earth of facts. I must admit, however, that in recent years the experimental
results have fitted theory so well that the effect has been rather the opposite.
But this is the way things have developed.
VII
Anyway, both these opposite ends - mathematics and experiments -
should teach us that there is only one danger for a physicist: becoming
narrow-minded and burying oneself too deeply in one's own world without
looking over its fence. We hope that we have contributed with this school
also to building bridges across these fences.
This school has now had a life of 25 years. Its founder has celebrated his
80th birthday last June. Let us hope that the school will reach the same age.
For the time in between: let us go on!
Graz, October 1986 H. Lata}
H. Mitter
VIII
Contents
Introduction to Kaluza-Klein-Theories
By M. Blau, W. Thirring, and G. Landi 1
Supersymmetry/Supergravity
By J. Wess .......................................... 29
Supersymmetric Yang-Mills Fields and Noncovariant Supergauges
By W. Kummer ...................................... 59
From Strings to Superstrings
By G. Veneziano (With 3 Figures) ......................... 95
Superstrings and Four-Dimensional Physics
By G.C. Segre ....................................... 123
Mass Issues in the Standard Model
By R.D. Peccei (With 12 Figures) ......................... 223
Critical Behaviour in Statistical QCD
By H. Satz .......................................... 283
Critical Behaviour in Random Field Gauge Theory
By H. Satz (With 7 Figures) ............................. 285
Experiments Beyond the Standard Model
By L.M. Lederman (With 26 Figures) ...................... 295
IX
Introduction to Kaluza-Klein-Theories
M. Blau 1, W. Thirringl, and G. Landi 2
lInstitut fur Theoretische Physik, Universitat Wien,
A-lOgO Wien, Austria
2Scuola Internazionale Superiore di Studi Avanzati, Trieste and
Gruppo Nazionale per la Fisica Matematica del Consiglio Nazionale
delle Ricerche, Italy
1. Introduction
In 1919 TH. KALZUA [1] made a r.emarkable observation. If one
considers Einstein's theory in 5 dimensions and calculates with
the ansatz
g II = 1, .•• 4, (1.1)
and g ll\! All o the curvature scalar R(5) in 5 dimensions one
,5 ,5
finds
Thus this Lagrangian reproduces exactly the coupled Einstein-Max
well equations. Ever since this unification came periodically into
fashion [2] and fell out of fashion again. And this in spite of the
fact that there has never been any experimental fact which either
verifies or falsifies this theory. Apart from a tiny electric di
pole moment for spin 1/2 particles [3] the theory says only Ein
stein + Maxwell (with some reservations to be discussed). What has
changed in the course of these purely psychological epidemics is
that what was mathematical and formal at the beginning acquired
more and more physical significance. If we really lived in a world
of 5 dimensions but the radius in the 5th dimension were very
small (order Planck length) then we would not see directly the 5th
dimension since excitations in x5 cost too much energy. The reason
why the fifth dimension is so small could be that the universe ex
panded anisotropically and has already collapsed in some directions
while it keeps expanding in others. Thus a realistic interpretation
of the ansatz (1.1) is thinkable and has sparked the most extra
ordinary speculations.
What has also changed since 1919 is that now we know electro
magnetism to be not an isolated phenomenon but only one component
of a non-abelian gauge theory which embraces at least the weak
interactions. Thus to make physics out of (1.1) at least such an ex
tension seems necessary.
In this introduction to these matters we shall comment on
various aspects of a realistic interpretation. In order not to
get too far astray we shall impose ourselves the following boundary
conditions:
I. We shall only consider pure gravity and not introduce extra
matter fields. The very purpose of Kaluza seems to us to reduce
everything to Einstein's theory. Of course, this cannot be done
at present and in particular how the fermions come in we will not
decide. This may either be through supergravity or through Kahler's
isomorphism between spinors and differential forms.
II. A realistic interpretation suggests that Einstein's vacuum
equations hold in this higher dimensional manifold. In other words
we shall discuss the physics of 4+0-dimensional Einstein spaces
which have the particular structure suggested by (1.1). Going with
this ansatz into R(4+0) from the very beginning, would lead to
Euler equations which might be weaker and we consider Einstein's
equations as the correct ones.
To give these lectures some scientific substance we set out to
prove the relevant theorems. To prepare the ground for that we have
to begin 'with a review of this century's differential geometry. Since
the purpose of our exercise is to unify gauge theories and gravi
tation we start with the notions common to both. For the convenience
of the reader we collect in the appendix the derivation of some
formulae needed in the text. In §3 we will summarize the features
of the originalS-dimensional Kaluza-Klein theory. Einstein's theory
is in sufficiently many respects different from Maxwell's theory
to raise questions how such a simple unification is possible. In §4
we shall consider higher-dimensional non-abelian extensions. Soon
we shall be discouraged by the following no-go-theorem: "A Ricci
flat Riemannian space with geodesic Killing vector fields has at
most an abelian continuous isometry group." Thus within our framework
there are no non-abelian extensions. This does not mean that we
have to abandon the whole idea that internal degrees of freedom
correspond to hidden dimensions of spacetime. There are many ways
out but none has the simplicity of the original ansatz (1.1).
2