Quantum Field Theory, as Simply as Possible

393 Pages·2023·31.184 MB·English

by  Zee A.

Q U A N T U M
F I E L D T H E O R Y,
A S S I M P LY
A S P O S S I B L E

Q U A N T U M
F I E L D T H E O R Y,
A S S I M P LY
A S P O S S I B L E
A . Z E E
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD
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Dedication
To all those who taught me quantum field theory, the theory of not quite
everything,directlyandindirectly１

Contents
Preface ix
Prologue:Thegreatestmonumentandaroadmapforaquest 1
I Our physical world 15
PreviewofpartI 15
1. Matterandtheforcesthatmoveit 17
2. Theriseoftheclassicalfield 22
3. Timeunifiedwithspace 34
4. Thegeometryofspacetime 47
5. Theriseandfallandriseofparticles 56
RecapofpartI 65
II The road to quantum field theory 67
PreviewofpartII 67
1. Gettingthebestdeal:fromleasttimetoextremalaction 69
2. Globalversuslocal 80
3. Enterthequantum 84
RecapofpartII 99
III Becoming a quantum field theorist 101
PreviewofpartIII 101
1. Howtobecomeaquantumfieldtheorist(almost)instantly 103
2. Originofforces:rangeandexchange 112
3. Attractionorrepulsion:amysteriousbutallimportantsign 123
RecapofpartIII 135
viii Contents
IV A universe of fields 137
PreviewofpartIV 137
1. Everybodyisafield:Diracsettheelectronfree 139
2. Theoreticalphysics,likemusic,startswithharmonybutthen
triestomoveon 149
3. Quantumelectrodynamics,perturbationtheory,
andculturaltaboos 162
4. Theroadtogaugetheory 173
RecapofpartIV 181
Awell-deservedrest 183
V Quantum field theory and the four fundamental interactions 185
PreviewofpartV 185
1. Antimatter! 187
2. Toostrongandtoomeanbutultimatelyfree 192
3. Theweakandtheelectroweakinteractions 211
AddendumtochapterV.3 239
4. Grandunification 243
5. Gravityandcurvedspacetime 261
6. Quantumgravity:TheHolyGrailoftheoreticalphysics? 279
RecapofpartV 295
VI Quantum field theory is more intellectually complete than
quantum mechanics 297
PreviewofpartVI 297
1. Aquestionofidentity 299
2. Exclusion,inclusion,andquantumstatistics 312
3. Intellectualcompleteness 324
RecapofpartVI 329
Partingcommentsandsomeunsolicitedadvice 331
Timeline 345
Ashortlistofmathematicalsymbols 347
Bibliography 351
Index 353
Preface
What is quantum field theory?
By now,there are numerous books introducing quantum mechanics2 to the
general public, but I am not aware of any popular book on quantum field
theory.3WhenItoldadistinguishedtheoreticalphysicistthatIwasworkingona
popularbookonquantumfieldtheory,heexclaimed,“Yourbookisreallygoing
tofillagap.Bynow,everybodyandhisgrandmotherhasheardaboutquantum
mechanics,butnobodyknowsanythingaboutquantumfieldtheory.”Ireplied,
“Exactly,butevenmorestrangely,bynoweverybodyandhisgrandmotherhas
heardaboutstringtheory.”Readersofpopularbooksonphysicshavejumped
directlyfromquantummechanicstostringtheory,itwouldappear.
Einstein showed, in 1905, that to describe particles moving close to the
speedoflight,weneedtomodifyoureverydaynotionsaboutspaceandtime
andunifythetwointoaspacetimedescribedbyspecialrelativity.Aroundthe
same time,it became apparent that the world of atoms and subatomic par-
ticles, such as the electron, is governed not by classical mechanics but by a
hithertounknownquantummechanics.
Considertheelectronorbitinginahydrogenatom,forexample.Whileit
behaveslikeaquantumparticleforsure,itmovesaroundratherslowly.Calcu-
lationsshowthattheelectronismovingatlessthan1%ofthespeedoflight.
Hence,specialrelativityisnotneeded4 tostudyhowitbehaves,forexample,
when absorbing and radiating light.Indeed,quantum mechanics was pieced
togetherslowlythroughmeticulousstudiesofhowatomsabsorbandradiate
light.
Backinthe19thcentury,FaradayandMaxwellintroducedtheelectromag-
neticfield,whichledtotheunderstandingthatlightisaformofelectromag-
netic wave.Thus,the electromagnetic field propagates through space at the
speed of light,and so,by definition,is relativistic.Hmm,the nonrelativistic
electronisinteractingwitharelativisticfield.
So, in elementary treatments of atoms radiating light based on quan-
tum mechanics, as it was formulated around 1925 and fed to unsuspecting