Elementary Particles and Their Currents

✍ Scribed by Jeremy Bernstein

• Publisher: W.H.Freeman & Co Ltd
• Year: 1968
• Tongue: English
• Leaves: 338
• Category: Library

✦ Synopsis

The plan of the book is as follows. The first chapter contains a brief review
of the elements of field theory, especially of the free fields. Apart from fixing
conventions on the Lorentz metric and the like, a sophisticated reader will not
learn much by reading it. In Chapter 2 the currents are introduced in a general
way and the connection between current conservation and an invariance group
is illustrated with the classical case of the group of invariances of a Lagrangian
containing two degenerate scalar fields the group SU2. Although this chapter
deals only with free fields we use throughout the LSZ technique for constructing
one-particle states via the asymptotic condition. The formulas are then easily
generalized to the interacting field case, and, in fact, the third chapter deals with
SU2 in the context of interacting pion-nucleon fields. In the fourth chapter we
turn on the electromagnetic field and study SU2 as a "broken symmetry."
With Chapter 5 the real work of the book gets underway. Here we begin
the study of electron-proton scattering. As the reader will discover, there is a
detailed analysis of the form factor structure of the matrix elements of the
currents as they are limited by Lorentz, parity, time reversal, and charge conjugation
invariance. I have chosen to treat the latter symmetries here, rather
than in the beginning of the book, since my own experience in reading texts
is that it is more convenient to have a general concept and its concrete applications
in close juxtaposition, whereas otherwise one tends to forget the former
before corning to grip with the latter. In Chapter 6 the experimental electronproton
situation is treated in a preliminary way and it is here that we first meet
the vector mesons. Historically the existence of the vector mesons was first
conjectured to explain the electron-proton scattering data. Only later were these
mesons actually found. In the seventh chapter there is a brief discussion of
dispersion relations, which are introduced mainly to give a logical foundation
to some of the formulas introduced in the previous chapters. I do not think that
dispersion relations "explain" anything in electron-proton scattering, but they
do provide a formalism for considering the structure of certain matrix elements
and for connecting one matrix element to another.
The next five chapters deal with the weak interactions of nonstrange particles.
The discussion divides naturally into the two parts of leptonic interactions
and semileptonic interactions. The former provide a perfect example of
the present impasse in theoretical elementary particle physics. The theory, as
is discussed in detail in the text, involves the coupling of currents to currents
and is in splendid agreement with experiment, but it suffers from an almost
complete absence of logical foundation. Leptons do not have strong interactions
but if we attempt to treat the current-current couplings in anything but lowestorder
perturbation theory, we are bedeviled by infinities of the worst sort.
Moreover, since the "weak photon" has not yet been observed, the basic role
of the currents must be regarded as mysterious.
It should be emphasized that even if the weak vector meson is found, this
will still leave open the mathematical problem of the structure of its theory,
especially in higher orders. In fact, the success of the lowest-order theory is
something of a handicap since, so far, experiment has not given any guidance
on how to construct the full theory. These matters are discussed, in some detail,
in Chapters 7 through 9.
The semileptonic weak interactions, such as ordinary 0-decay, involve
both lepton and baryons in initial and final states. Because of this, semileptonic
decays combine aspects of both the strong and the weak interactions. Chapter
10 treats the vector current part of the semileptonic coupling, which is given,
as we shall see, by the isotopic vector part of the electromagnetic current. The
vector current is conserved so long as SU2 is an approximately valid symmetry
group. In this chapter I review the consequences of this property of the current.
Because the vector current can be identified with the isotopic spin current
one is spared the problem of the details of the strong couplings, since one may
take the unknown form factors in 0-decay matrix elements from electronproton
scattering experiments. However, with the axial vector current there is
no such luck, and in Chapters 11 and 12 I review the various attempts at making
dynamical models for the axial current. I have included a selection of "proofs"
of the Goldberger-Treiman relation and an introduction to the current algebra
of SU2 X SU2. An exploitation of this algebra leads to the discovery of the
celebrated Adler-Weisberger sum role, which is derived in Chapter 12.
The rest of the book deals with the weak and electromagnetic interactions
of strange particles. Chapter 13 is a general introduction to SU3, which now
appears to be the correct approximate symmetry group of the elementary
particle Lagrangian. Chapter 14 contains a review of some of the calculations
using naive quark models. Chapter 15 considers the Cabibbo theory of strange
particle decays and some of the results of the SU3 X SU3 current algebra. At
the very end of the book the reader will find a discussion of CP violation in
the K°, K° system

✦ Table of Contents

Chapter 1 Introduction and Notation

Chapter 2 Currents: A First Look

Chapter 3 Interacting Fields

Chapter 4 Turning on the Electromagnetic Field

Chapter 5 Electron-Nucleon Scattering I: Form Factors C, P, T, and CPT

Chapter 6 Electron-Nucleon Scattering II

Chapter 7 Dispersion Relations and Electron Scattering

Chapter 8 The Weak Interactions I: Mostly Leptons

Chapter 9 The Weak Interactions II: Nucleons

Chapter 10 Weak Currents: The Vector

Chapter 11 The Axial Vector I

Chapter 12 The Axial Vector II

Chapter 13 Strange Particles: An Introduction to SU3

Chapter 14 More on SU3

Chapter 15 Decays that Change Strangeness

Index