Relativistic Quantum Mechanics Bjorken Drell (1964)

309 Pages·1964·14.303 MB·English

by  J.D.Bjorken S.D.Drell

I3elativistic
Gl,uantum
Meehanies
INTERNATIONAL SERIES IN PURE AND APPLIED PHYSICS
Leonard I. Schifr, ConsultingE ditor
Allis and, Herlin Thermodynamicsa nd St'atisticaMl echanics
Becker Introduction to'l'heoretical Mechanics
Bjorken and DreII RelativisticQ uantum Mechanics
Clark Applied X-raYs
Coltin Field Theory of Guided Waves
Eaans The Atomic Nucleus
Finkelnburg Atomic PhYsics
Ginztoi MicrowaveM easurements
Green NuclearP hYsics
Curney Introduction to StatisticalM echanics
Hatl Introduction to Electron Microscopy
Hard,y ancl Percin The Principles of Optics
Harnwell Electricity and Electromagnetism
Harnwell and Liaingood ExperimentalA tomic Physics
Ilarnwell and' Stephens Atomic Physics
Henley and Thirring Elementary Quantum tr'ield Theory
Houston Principleso f MathematicalP hysics
Hund High-frequencyM easurements
Kennard, Kinetic TheorY of Gases
Lane SuperfluidP hYsics
Leighton Principleso f Modern Physics
Lind,say MechanicalR adiation i
Lioingston and Blewett ParticleA ccelerbtors
Middieton An Introduction to StatisticalC ommunicationT heory
Morse Vibration and Sound
Morse and Feshbach Methods of Theoretical Physics
Muskat Physical Principles of Oil Production
Present Kinetic Theory of Gases
Read Dislocations in Crystals
Richtrnyer, Kennard, and. Lauritsen Introduction to Modern phvsics
Schiff QuantumMechanics
Seitz The Modern Theory of Solids
Slater fntroduction to Chemical Physics
Slater Quantum Theory of Atomic Structure, Vol. I
Slater Quantum Theory ofAtomic SJructure,V ol. II
Slater Quantum Theory of Matter
Slater Quantum Theory of Molecules and Solids,V ol. I
Slater Quantum Theory of Molecules and Solids, Vol. 2
Sla,ter and Frank Electromagnetism
Slater and, Franh Introduction to Theoretical phvsics
Slater and Frank Mechanics
Smythe 'Static and Dynamic Electricity
Strdtton r.ElectromagneticT heory
Tinkharn Group Theory and Quantum Mechanics
Tounes and, Scha.u:Iow Microwave Spectroscop]r
White Introduction to Atomic Spectra
The late F. K. Richtmler lvas consulting Editor of the seriesl rom its inception in
1929 to his death in 1939. Lee A. DuBridge was consulting Editor from r9J9
tro l!46; aud G. P. Harnwell from 194? to I9S4.
James D. Bjorken Sidney D. Drell
Associate ProJessor
S tanJ ord. Linear Accelerqtor Center
StanJord' Unioersity
McGraw-Hill Book Cornpa,ny
Nero York St. Louis Scln Francisco Toronto Lond'on S5rd'ney
R,elativistic
Gl,uanturn
,
Meehanies
5 tc'\a
J :rA,
bta t''no
Relativistic Qtrantum Meohanice
copyright @ 1964 by McGraw-Hill, Inc. All Rights Reserved. printed in
the United States of America. This book, or parts thereof, may not be
reproducedi n any form without permissiono f the publishers.
Library of CongressC atalog Card Number 6B-ZLZZ}
78 9 101 11 2-MAMM- 7 5 43 2 LO
05493
\
Preface
The propagutor,'approach to a relativis\ic quant'um theory. pioneered
in rg+g by Feynman has provided a practical, as well as intuitively
appealing, formulation of quantum electrodynamics and a fertile
approaclt to a broad class of problems in the theory of elementary
putti"t".. The entire renormalization program, basic to the present
confidence of theorists in the predictions of quantum electrodynamics,
is in fact dependent on a Fe5rnman graph analysis, as is also con-
siderable progr"u. in the proofs of analytic properties required,to write
dispersion relations. Indeed, one may go so far as to adopt the
extreme view that the set of all Feynman graphs is the theory'
we do not advocate this view in this book nor in its companion
Prcfaee
Yllt
volume, "Relativistic Quantum !'ields," nor indeed do we advocate
any single view to the exclusion of others. The unsatisfactory status
of present-day elementary particle theory does not allow one such a
luxury. In particular, we do not, wish to minimize the importance of
the progress achieved in formal quantum field theory nor the con-
siderable understanding of low-energy meson-nucleon processesg iven
by dispersion theory. However, we give first emphasis to the develop-
ment of the Feynman rules, proceeding directly from a particle wave
equation for the Dirac electron, integrated with hole-theory boundary
conditions.
Three main convictions guiding us in this approach were the
primary motivation for undertaking this book (later to become books):
1. The Feynman graphs and rules of calculation summarize
quantum field theory in a form in close contact with the experimental
numbers one wants to understand. Although the statement of the
theory in terms of graphs may imply perturbation theory, use of
graphical methods in the many-body problem shows that this formal-
ism is flexible enough to deal with phenomena of nonperturbative
character (for example, superconductivity and the hard-sphere Bose
gas).
2. Some modification of the Feynnian rules of calculation may
well outlive the elaborate mathematical structure of local canonical
quantum field theory, based as it is on such idealizations as fields
defined at points in space-time. Therefore, let us develop these rules
first, independently of the field theory formalism which in time may
come to be viewed more as a superstructure than as a foundation.
'
3. Such a development, more direct and less formal-if less com-
pelling-than a deductive field theoretic approach, should bring
quantitative calculation, analysis, and understanding of Feynman
graphs into the bag of tricks of a much larger cornmunity of physicists
than the specialized narrow bne of second quantized theorists. In
particular, we have in mind our experimental colleagues and students
interested in particle physics. We believe this would be a healthy
development.
Our original idea of one book has grown in time to two volumes.
In the first book, "Relativistic Quantum Mechanics," we develop a
propagator theory of Dirac particles, photons, and Klein-Gordon
rnesons and perform a series of calculations designed to illustrate
various useful techniques and concepts in electrornagnetic, weak, and
strong interactions. These include defining and implementing the
renormalization program and evaluating effects of radiative correc-
Preface
lx
tions, sucha s the Lamb shift, in low-order calculations. The recessary
backgroundf or this book is provided by a coursei n nonrelativistic
quantum mechanicsa t the generall evel of schifl's text ,,euantum
Mechanics."
,,Relativistic
In the secondb ook, euantum Fields,,,w e develop
canonical field theory, and after constructing closed expressionsf or
propagators and for scattering amplitudes with the LSZ reduclion
technique,r eturn to the Feynman graph expansion. The perturbation
expansion of the scattering amplitude constructed by canonical field
theory is shown to be identical with the Feynman rules in the first
book. with further graph analysis we study anaryticity properties of
Feynman amplitudes to arbitrary orders in the coupling parameter
and illustrate dispersionr elation methods. Finally, we prove the
finitenesso f renormalizedq uantum electrodynamicsto each order of
the interaction.
Without dwelling further on what we do, we may list the major
topics we omit from discussionin theseb ooks. The developmento f
action principlesa nd a formulation of quantum field theory from a
variational approach,s pearheadedla rgely by schwinger,a re on the
whole ignored. we refer to action variations only in search of sym-
metries. Therei s no detailedd iscussiono f the powerfuld evelopments
in axiomatic field theory on the one hand and the purely g-matrix
approach,d ivorced from field theory, on the other. Aside from a
discussiono f the Lamb shift and the hydrogen atom spectrum in the
first book, the bound-statep roblem is ignored. Dynamical applica-
tions of the dispersion relations are explored only minimaliy. A
formulation of a quantumf ield theory for massivev ector mesonslsn ot
given-nor is a formulation of any quantum field theory with deriva-
tive couplings. Finally, we have not prepared a bibliography of all
the significant original papers underlying many of the developments
recordedi n theseb ooks. Among the following recent excellenib ooks
or monographs is to be found the remedy for one or more of these
deficiencies:
Schweber, S.: "An Introduction to Relativistic euantum Field Theory,r' New
York, Harper & Row, Publishers,I nc., 1961.
Jauch, J. M., and F. Rohrlich: "The Theory of photons and Electrons." cam-
bridge, Mass., Addison-WesleyP ublishing Company, Inc., 1g5b.
Bogoliubov, N. N., and D. v. shirkov: "Introduction to the Theory of euantized
Fields," New York, fntersciencep ublishers, Inc., Lg5g.
Akhiezer, A., and V. B. Bereztetski: .,euantum Electrodynamics,', 2d ed., New
York, John Wiley & Sons,I nc., 1g68.
umezawa, H.: "Quantum Field rheory," Amsterdam, North Hoiland pub\shing
Company, 1956.
PreJace
Eamilton, J.: "Theory of Elementary Particles," London, Oxford University
Press, 1959.
Mandl, F.: "Introduction to Quantum Field Theory," New York, Interscience
Publishers,I nc., 1960.
Roman, P.: "Theory of Elementary Particles," Amsterdam, North Holland
Publishing Company, 1960.
Wentzel, G.: "Quantum Theory of Field," New York, Interscience Publishers,
Inc., 1949.
Schwinger, S.: "Quantum Electrodynamics," New York, Dover Publications,
Inc., 1958.
Feynman, R. P.: "Quantum Electrodynamics," New York, W. A. Benjamin,
Inc., 1962.
Klein, L. (ed.): "Dispersion Relations and the Abstract Approach to Field Theory,"
New York, Gordon and Breach, ScienceP ublishers,I nc., 1961.
Screaton, G. R. (ed.): "Dispersion Relations; Scottish Universities Summer
School," New York, InterscienceP ublishers,I nc., 1961.
Chew, G. F.: "S-Matrix Theory of Strong Interactions," New York, W. A'
Benjamin, Inc., 1962.
fn conclusionw, e owet hanks to the many studentsa nd colleagues
who have been invaluable critics and soundingb oards as our books
evolved from lectures into chapters,t o Prof. Leonard I. Schiff for
important initial encouragemenatn d supportt o undertaket he writing
of these books, and to RosemarieS tampfel and Ellen Mann for
marvelouslyc ooperatives ecretariahl elp.
JamesD . Iljorken
Sid,neyD . Drell