Recent Developments in Particle and Field Theory: Topical Seminar, Tübingen 1977

421 Pages·1979·8.391 MB·German

by  Henry D. I. Abarbanel (auth.), Walter Dittrich (eds.)

Walter Dittrich (Ed.)
Recent Developments
in Particle and
Field Theory
Topical Seminar, TObingen 1977
With 86 Figures
Friedr. Vieweg & Sohn Braunschweig /Wiesbaden
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Recent developments in particle and field theory
Walter Dittrich (ed.). - Braunschweig, Wiesbaden:
Vieweg, 1979.
ISBN-13 :978-3-528-08426-4 e-ISBN-13:978-3-322-83630-4
DOl: 10.1007/978-3-322-83630-4
NE: Dittrich, Walter [Hrsg.)
1979
All rights reserved
© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1979
Softcover reprint of the hardcover 1st edition 1979
No part of this publication may be reproduced, stored in a retrieval system or transmitted,
mechanical, photocopying or otherwise, without prior permission of the copyright holder.
ISBN-13:978-3-528-08426-4
Preface
This is a collection of lectures and seminars delivered at the "Symposi
um on Particles and Fields" held at TUbingen University, West Germany,
from June 20th to July Pt, 1977, on the occasion of the University's
sooth anniversary.
We were very fortunate that so many excellent colleagues from Europe
and the U. S. contributed their ideas to this meeting, whose main pur
pose ist was to cover a brod spectrum of the various aspects in the
current development of particles and fields, rahter than to focus on a
single subject. It was interesting to see source-, quark-, and string
people side by side attacking the very same unsolved problems in
particle physics. Exchange of ideas and techniques between the diverse
representatives of field- and particle physics was the principal goal of
the meeting.
Last not least, we are most grateful to the President of our University
A. Theis, and his assistant, H. E. Lang, for the generous support that
enabled us to make this symposium a profitable and pleasant experience
for all of us.
The Editor
Walter Dittrich
This volume is dedicated to
the memory of
Benjamin Lee
Contents
H. Abarbanel
Using Field Theory in Hadron Physics
R. Blankenbecler
Composite Hadrons and Relativistic Nuclei .................. 43
S. J Chang
Vacuum Tunneling in Minkowski Space .................... 105
S. J Chang
Hartree Approximation in Field Theory 129
H. M. Fried
Two Topics in Eikonal Physics ........................... 147
K Johnson
The Static Potential Energy of a Heavy Quark and Anti Quark 175
A. Neveu
Semiclassical Methods in Field Theory 185
F Rohrlich
Lectures on the Relativistic String . . . . . . . . . . . . . . . . . . . . . . . .. 197
J Schwinger
Introduction and Selected Topics in Source Theory ........... 227
W. Becker and D. Grofter
Confinement, N onlocal Field Theory, and Electromagnetic
Interaction .......................................... 335
W. Becker and D. Grofter
Supergravity and a Problem Raised by ITS S-Matrix ........... 351
W. Dittrich
Quantum Mechanical Corrections to the Classical Maxwell
Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 357
M. P. Fry
Spoor of a Fixed Point in QED ........................... 365
H. G. Latal
Quantum Theory of Synchrotron Radiation ................. 375
J Rafelski
Self-Consistent Quark Bags .............................. 385
- 1 -
Using Field Theory in Hadron Physics
Henry D. I. Abarbanel
Fermi National Accelerator Laboratory, Batavia, Illinois 60510
- 2 -
I. Introduction
This decade has seen a marvelous return to quantum field theory among
theorists in high energy physics. The compelling beauty of non-Abelian gauge
theories, the striking empirical support for spontaneous symmetry breaking in weak
interaction theories, the deep connection between asymptotic freedom and the
approximate scaling in inelastic lepton scattering on hadrons, the entrancing
suggestion of quark confinement-all this and more has drawn our focus once again
on quantum field theories. We have learned to view field theory as providing us
with fundamental degrees of freedom rather than thinking that each new particle
or resonance as requiring a new field for its description. Indeed the idea that some
small set of degrees of freedom (quarks and gluons) provides the basis for all
observed mesons and baryons seems to be a concrete realization of the ideas of
"nuclear democracy" advocates of the last decade. [Increasing numbers of them
have been seen with path integrals and Lagrangians lately. 1 It makes explicit the
concept that all hadrons are composites; not of each other, though through
unitarity all the hadrons can become the other hadrons within the restrictions of
conservation of charge, baryon number, isospin, etc. It is a deeper way: they are
all composites of quarks and gluons.
These lectures have no pretentions to cover all possible topics in the
connection of field theory and hadron physics. Rather the goal is much more
modest: I hope to touch on a number of tantalizing questions which will serve to
some extent as an introduction for the student as well as the research person
curious for more than a peek. Several "old" topics will be treated-the
renormalization group and the infrared and ultraviolet limits of field theory,
choosing Quantum Chromodynamics (QCD) from among all theories, various
thoughts on spontaneous mass generation. Some newer ones are discussed here
too-ideas on color confinement, instantons and the vacuum state in QCD, and
related topics.
- 3 -
As general background material I recommend the article on "Gauge Theories"
by E.S. Abers and B. W. Lee, Physics Reports 9C, 1 (1973); the lectures by S.
Coleman at the 1975 Erice Summer School; the book by J.C. Taylor, Gauge
Theories of Weak Interactions (Cambridge U. Press, 1976); and the review article
by R. Jackiw, Rev. Mod. Phys. 49, 681 (1977).
II. The Renormalization Group and Some Consequences
Quantum field theories of relevance to particle physics all have divergences
when one calculates in perturbation theory about the free theory characterized by
propagators
(Spin Numerator)/(m2 _ p2 - it:) (1)
Such theories are not defined by the classical Lagrange density; one has to give a
prescription for making the theory finite in every order of perturbation theory
before a calculational procedure of recognizable validity emerges. The generally
accepted manner for doing this is to define the theory by giving the value of a few
basic quantities (mass, coupling constant, ••• ) at some point in momentum space. So
one takes the original theory defined by the classical Lagrangian and renormalizes,
so the divergences are absorbed in scales of wave functions (or field operators) and
other physically harmless locations. Since there is an enormous arbitrariness in
how, precisely, one renormalizes, we can anticipate an invariance of physical
quantities on changing the point in momentum space where that renormalization is
done. The expression of that invariance is the renormalization group. The behavior
of classes of quantum field theories under this group allows one to select those with
controllable infrared or ultraviolet behavior and thus on the basis of the behavior of
experiments which probe long or short wavelength phenomena to choose acceptable
field theories.
- 4 -
To illustrate this in action let's look at a scalar field in D dimensions of
space-time with Lagrangian density
(2)
When AO is dimensionless, namely when N =2 D/(D - 2), all the divergences of
quantities expanded in a perturbation series in Ao are logarithmic and the theory
can be renormalized, i.e. made finite, by redefining the field
(3)
and coupling
(4)
where the dimensionless (infinite) factors Z and ZA are constructed so all Green
functions in the theory are finite. These renormalization factors are defined by
gl.v.m g th e va1 ue 0f cter ·am Gr een f unc t·I ons a t some po.m t p 2 =- ]J2 ,]J 2 > 0 , m.
momentum space. These Green functions are given by
(n) D ~
GO (PI,···P,AO)o (LP·)
n j=l J
(5)
d
To lowest order in AO we have for G(2) and N)
- 5 -
G(2){p2, /'I0. ) = 1°/ ( P2 + I0E: ) (6)
and
(7)
We define renormalized Green functions by
G( n){ Pl' ••• Pn,A,11 ) (8)
and require (this is the renormalization)
I
z _a
21° G 0 (2)( p2, ).. 0 )-1 ' (9)
ap
2 2
P =-11
and
-i)..
{I 0)
(2TlP/2 (N-2)
I
ZN/2G (N){po,).. ) (ll)
o J 0 2 2
P =- 11
These determine Z and then Z).. once one has calculated GO (2) and GO (N) to
whatever accuracy desired using perturbation theory in ).. 0 and some method of
cutting of the divergence integrations. After rescaling by Z Cind Z).. via (3) and (4)
the cutoff is sent to infinity with $,).., and 11 held fixed. What is remarkable, then,
is that the resulting theory is then finite to all orders in A.