Student Friendly Quantum Field Theory: Basic Principles & Quantum Electrodynamics

544 Pages·2013·13.718 MB·English

by  Robert D. Klauber

StudeFnrti endQluya ntuFmi elTdh eory
BasiPcr inciapnldeQ su antuEml ectrodynamics
Copyrig©h otf R oberDt.K lauber
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To
thes tudents
May thefiyn dt hitsh ee asieasntd,t hutsh em oste fficient,
physitcesx tto l earnf romt hatth ehya vee veurs ed.
"Oafl tlhc eo mmunaivtaiieltsaou b stl heei rnseo o tn Iew ould
wanttod evomytsete olfe, x cfeoptrth s eo cioeftty ht er ue
searcwhheirhcsah,vs e ryf elwi vmienmgb earta snt yi m"e .
AlbertE inesitn
TabloefC ontents
TabloefW holeneCshsa r.t.s. ..........i..x. ...P.a..r.Ot.n .e.:F. r.e.eF. .i.e.l.d.s 39
......................................
Prefa...c...e.... ........................................................ xi 3.S calaSrpsi:n0 F ield.s. ....... 40
... ....... ..... . .......
Preerquisi.t.e.s. .................x.v. .......3...P0.r .e.l.i.m.i.n..a..r..i..e..s.. .....................4 .0. ...............................
Acknowledgem.e.n.t.s. ............x.v. .......3...R1.e .l.a.t.i.vQ.iu.sa.tn.it.cu.M m.e .c.h.a.n ics:
A HistoLreys s.o.n ..........4.1. ........................
3.T2h eK lein-GoErqduoant iionn
QuantuFmi eTlhde o.r.y. .......4.7. ..................
Preparation 3.C3o mmutatRieolna tiTohnesC :r uxo fQ Ff 51
...
1.B irdE'yse V iew. ................. .1. 3.T4h eH amiltoniinQa Ffn ..........5.3. ...................
..... .... ...... ........ 3.E5x pectaVtailounea sn dt hHea miltonia5n7
1.P0u rpoosfet hCeh apt.e.r.. ............,. 1 ......
. .. .. .. .. .. .. ..... 3.C6r eataionndD estrucOtpieorna tors. .58
1.T1h iBso ok'Asp proatcoQh Ff ........1. ........ .. ..
. ....... . ... . . 3.P7r obabiFloiutCryu ,r renatnsd,
1.W2h yQ uantuFmi elTdh eor.y....?.. ................. .1 ChargDee nsity . 61
.............. ..........................
1.H3o wQ uantuFmi eTlhde or.y...?... ........ ........ I. . 3.M8o reo nO bserva.b.le.s. ........6.3. ......................
1.F4r om WheCnrceea tainodn 3.R9e aFli el.d.s. ..............6.5. ..................................
DestrucOtpieorna to..r.s?.. .. ...3. ...
. .... .. ......... 3.1C0h aracteroifKs lteiicns- GoSrtdaotne s6 5
1.O5v erviTehwe:S tructoufPr hey sics .......
andQ Ff'sP lacTeh ere.i.n. ......3. .......3...1O.1d. d.sa. n.dE. n.d..s.. .............6.6. ............................
1.C6o mpariosfoT nh reQeu antum The.o..r5ie s 3.1H2a rmonOiscc illaatnodQr Ffs .......6.9. ..........
. . ...
17.M ajor CompoonfeQ nFf t.s. ........8. ......3...1.3. .ST.ch.ae.l Fa.er.y .n.m aPnr opaga.t.o.r. ..7.0. .........
1.P8o inttosK eepi nM ind ....... ...8. 3.1C4h aptSeurm mar.y. ...........7.8. .........................
...... ....... . ........ ..
1.B9i gP ictuorfOe u rG oa.l. .........8. .......3...1A.5p. p.e.n.dA.i:.xK .l.e.in.-.G.o Erqduoant ion
froHm. PE.q uatioofMn o tio.n . 79
1.1S0u mmaroyft hCeh apte.r. . ...9 ... .......... ...
.. ................... ... . 3.1A6p pendBi:xV acuuQmu antaan d
1.11S uggesti.o...n...s...?..... .............................. 9. ... HarmonOiscc ill.a.to.r.s. ......8.0. ...................
1.1P2r oble.m.s. ...............9. ......3...1.A7p. p.e.n.d.Ci.:xP. r.o.p.a.g.aD.te.orr.i v.a.t.i.o.n. ......
2.F oundatio.n.s. ..........................1.1 Ste4pf o.1.r- ...................•.......................... 81
... .... ... ... .. . .. 3.1A8p pendDi:xE nlargtihnIegn tegration
2.C0h aptOevre rvi.e.w. ..........1.1. ..........P.a.to.hf .F i.g.3..- ..6.. .............. ....8.1. ..........................
2.N1a turUanli tasn dD imensi.o.n.s. ....1.1. ......3...1P.9r. o.b.l em.s ... ..82
..... .................. . . ......... ......... .....
2.N2o tat.io.n. ...............1.5. ....................................
2.C3l assivcsQa ula ntuPml anWea ves. . .1 6 4.S pinorSsp:i 1n/ F2i el.d.....s... ........ .............. 84
.. .. .......
2.R4e vieowfV ariatiMoentahlo .d.s .....1.7. ......4...P0.r .e.l imin...a...r...i....e. s.. ......... ............. ........... 84
2.C5l assiMceaclh aniAcns O:v ervi.e.w. ..1.9. ......4.. R1e lativQiusatnitcuM me chanics
2.S6c hrodivnsgH eeri senbPeircgt ur.es. .2.5 foSrp ino...r....s... ............. ............. ............ 85
.. ...... .
2.Q7u antuTmh eorAyn:O vervi.e.w. ....2.9. ......4..T.2h. e.D iraEcq uatiionQn u antum
FielTdh eor.y. ............1.0.3. ..........................
2.C8h aptSeurm mar.y. ...........3.1. ..........................
4.A3n ti-commutRaetliaotni ons
2.A9p pendix: Understanding Contravariantf oDri raFci el.d.s. ..........1.0.4. .......................
andC ovariCaonmtp one.nt.s. .....3.2. ............
4.T4h eD iraHca miltoniinQa Ffn 105
2.1P0r oble.m.s. ........... ..... .36 ...................
.. .... .. . .. .. .. ........ . . ...... .. 4.E5x pectaVtailounea sn dt he
DiraHca miltonia.n. . 109
........ ....... ................
4.C6r eatainondD estrucOtpieorna to.rs .1 09
.... ......
4.7
QFf SpinCohra rgOep erator
andF ouCru rren.t .. .1 11
..... ........... .......... .......
4.D8i raTch reMeo mentuOmp erato.r ..113
.... ...... ..
4.D9i raScp iOnp erationQr Ff ..... . .1 13
.. .. . ........ ....
VI
4.1Q0F f HelicOipteyr at.o.r. .........l.I.S. ....P.a.r.Tt.w .o..:I. n..t.e racFtiienlgd s 181
........................
4.1O1d dsa ndE nds. ...............l.I.S. .......................
7.I nteractTihoenU sn:d erlyTihnego ry1 82
....
4.1T2h e Spinor FePyrnompaang a.t.o.r. ..1.1.7. .....
7.0P relimin.a.r.i.e.s. ...........1.8.2. ...........................
4.1A3p pendAi.xD iraMca tricaensdu ,.v,,
Relati.on.s.. ................1.2.2. .......7...1I. n.t.e.r.a.c.ti.ni.R o enlsa tivistic
..... . . .
QuantuMme chani.c.s. .........1.8.3. ................
4.1A4p pendBi.xR elativSipsitniG:ce tting
tot heR eaBlo ttoomf I tAI L ..................1 24 7.2I nteracitniQ ounasn tuFmi elTdh eor.y.. ....1.8 6
4.1P5r oble.m.s.. .............................................1.3.1 7.3T heI nteracPtiicotnu. .r....e... ................1.8.7. ....
S S
7.4T he Operataonrdt he Matrxi. .........1..9 4
5.V ectorSsp:i 1n F ields 134 ... . .
.............................. S
7.5F inditnhge Operat.o.r. . ......197
................ ... ...
5.0P relimin.a..r....i..e...s.. .................................1 34 7.6E xpandiSnIgI I'('I" 200
••••••••••. .....•••••••••..•••••.•••• •••••••
5.1R evieowf C lassiEclaelc tromagn.e.t.i1 s3m5
.... 7.7W ick'Tsh eoreAmp plied to
5.2R elativistic MQeucahnatnuimc s DysonE xpansi.o.n. .....:.. .........2..0..1.. ..........
forP hoto.n.s. ..............1.4.4. .........................
7.8J ustifWyiincgk 'Tsh eore.m. ................2.0 4
. .. . ..
5.3T heM axwelElq uatiionn
7.9C ommenotn N ormaOlr derionftg h e
QuantuFmi elTdh eor.y. ........1.4.7. ..............
HamiltonDieanns i.t.y. .........2.0.9. ................
5.4C ommutation RefloarPt hiootnosFn i el.d.1s 4 8
7.1C0h aptSeurm mar.y. ............2.1.0. .....................
5.5T heQ Ff HamiltonfioarPn h oto.ns. ...149
... ..... 7.1A1p pendiJxu:s tifWyiicnkg' Tsh eorem
5.6O thePrh oton OperianQt Fofr. s.... ........ 1.4.9. .. viaI nduct.i.o.n. ....................................... 210
5.7T heP hotoPnr opaga.t.o.r. ........I.S.O. .......7...1.P2.r .o.b.l.e..m. s. ................2.1.2. ..............................
5.8M oreo nQ uantizaatnidoP no lariza.t.i.1o.5n.0 .
8.Q ED:Q uantuFmi elIdn teraction
5.9P hotoSnp iIns suSeism iltaoSr p ino.r.s. .1.5.4. .
TheorAyp pliteodE lectromagne2t1i4s m
...
5.1W0h eret oN ext.?. .............I.S.S. .......................
8.0P relimin.a.r.i.e.s. ...........2.1.4. ...........................
5.1S1u mmarCyh ar.t. .............I.S.S. .......................
8.1D yson-WicEkx'psa nsifoonrQ ED
5.1A2p pendiCxo:m pletenReeslsa ti.ons. 160
........ HamiltonDieanns i.t.y. .........2.1.5. ................
5.1P3r oble.m.s. ................1.6.1. .........S.(.){. .................
8.2 Physica.l.l.y. .............2.1.7. .........................
()I
6.S ymmetrIyn,v ariance, 8.3S Physica..l..l...y.. ...................................2 .17
andC onservaftoiroF nr eFei el..d....s.... 162 8.4S ( �)P hysica.l.l.y. .............2.2.0. .........................
6.0P relimin.a.r.i.e.s. ............1.6.2. .......8...5T. h.e.S h.o.r.t.c.u.t. ..M.eF.te.hy.on.dm :aR nu le.s... .2.3.5.
6.1I ntroducttoSi yomnm etr.y.... ........ ..............1 63 8.6P ointtosB eA wareo f.. ......... ..................... 2.37
6.2S ymmetriynC lassiMceaclh ani.cs. ...1.6.7 8.7I ncludOitnhge Crh argeLde ptoinnsQ ED .2.4 1
.......
6.3T ransformaitniQ ounasn tuFmi elTdh eor1y7 1 8.8W hent oA ddA mplituadneds
Whent oA ddP robabil.i.t.i.e..s.. .142
6.4L orenStyzm metroyft he ............
LagrangDieanns i.t.y. .........1.7.1. .......8...9W. a.v.e.P .a.c.k.e atnsd C ompleSxi nuso.i..d....s2 43
6.5O theSry mmetrioefts h eL agrangian 8.1L0o okinCgl oseartA ttraction
DensitNyo:e theTrh'eso re.m. .....1.7.2. ........ andR epuls.i.o.n. ...........2.4.3. .......................
6.6S ymmetrGya,u gesan,d G augeT heor.y 177 8.11 TheD egreoeft heP ropagaCtoonrt ribution
.....
tot heT ransitAimopnl itu..d.e. ........2..4.6.
6.7C haptSeurm mar.y. .............1.7.8. ..................... . . . .
8.1S2u mmaroyf W hereW e HaveB een:
6.8P roble.m.s. .................1.7.9. ..............................
Chaps7. a nd8 ...............2.4.7. ......................
8.1P3r oblem.s. .................... 252
... .... .. .... .. . ...... .. ......
9.H igheOrr deCr orrections 254
......................
9.0B ackground. .. ..... ...254
....... ................... . ...........
9.1H igher OCrodrerre ctTieornm s ...2.5 5
..............
9.2P roblems 265
......................................................
Vll
10.T heV acuumR evisited 267 Part ThrReeen:o rmaliza-tTiaomni ng
...........................
ThosNeo torioIunsfi nities 303
10.B0a ckgrou.n.d. ...............2.6.7. .......................... ................
10.V1a cuumF luctuatTihoenT sh:e or.y. ......... 21627O. v ervioefwR enormalization 304
................
10.V2a cuum FluctuaantdEi xopnesr ime.n.t2..7..0
12.P0r elimin.a.r.i.e.s. ...........3.0.4. .........................
10.F3u rthCeorn sideraotfi ons
12.1 WhetnhceTe e rm" Renormaliza.t.i.3o.0n5." ?
UncertaiPnrtiyn ci.p.l.e. .......2.7.2. ...............
12.A2 BrieMfa thematiIcnatle rlude:
10.W4a veP acke.t.s. ..............2.7.4. ........................
Regulariz.a.t.i.o.n. .........3.0.5. .......................
10.F5u rthCeorn sidera.t.i.o.n.s. ......2.7.7. ...............
12.A3 RenormalizEaxtaimopnl e:
10.C6h apter Sum.m.a.r.y. .........2.7.7. ....................
Bhabha Scat.t.e.r.i.n.g. ......3.0.6. ...................
10.A7d dend.a. .................2.7.7. ..............................
12.H4i gheOrr deCro ntributiino ns
10.A8p pendAi:xT heoretViaclaulfe o r BhabhSac atte.r.i.n.g. .............................. 310
VacuumE nergDye nsi.t.y. ......2.7.9. ............
12.S5a meR esuflotrA nyI nterac.t.i.o.n. .3.1.2. ......
10.A9p pendBi:xS ymmetrByr eakiMnags,s
12.W6e AlsoN eedt oR enormalMiazses. ...3.1.2. .
Terms, Vaancdu umP air.s. .......2.8.0. ..........
12.T7h eT otaRle normalizSacthieomn.e . ..3.1.3. ...
10.10 AppeCn:dC iomxp arisoofQn F f for
12.E8x prees( sk a)s e (P )o r
DiscrevtsCe o ntinuous Soluti2o8n1s ..........
OtheSry mboflo rE nerg.y. .......3.1.3. ...........
10.1A1p pendDi:xF reFei elds and
12.T9h ingYso uM ayR unI nt.o. .......3.1.7. ............
"Pair Popping" .R.e.-.v.i.s.i.t.2e.8d.4 . ..........
12.1A0d iabaHtyipco the.s.i.s. .......3.1.8. ................
10.1P2r obl.e.m. ................2.8.5. .............................
12.1R1e gularizRaetviiosni .t.e.d. ......3.1.9. ............
11.S ymmetrIyn,v ariaanncde ,
12.1W2h ereW e Stan.d. ............3.1.9. .....................
ConservaftoiroI nn teracFtiienlgd s2 86
...... 12.13 Chapter .S.u.m.m.a.r.y. ......3.2.0. ...................
11.P0r elimin.a.r.i.e.s. ...........2.8.6. .......1.2...1P.4r. o..b.l.e..m..s.. ............. .........3.2.1. ............................
I1 .1A HelpfMuold ificattoit ohneL agrang2i8a7n
13.R enormalizTaotoilokni t 322
11.E2x ternSaylm metrfyo rI nteracFtiienlgd2 s8.9 ........................
13.P0r elimin.a.r.i.e.s. ...........3.2.2. .........................
11.3I nterSnyamlm etrayn dC onservation
forI nterac.t.i.o.n.s. .........2.9.0. .......1.3...T1.h .eT. h.r.e.Ke.e .y.I .n.t eg.r.a.l.s. ......3.2.2. ..............
11.G4l obavlsL ocaTlr ansformations 13.R2e latiWoen'sl Nle ed. ...........3.2.5. .................
andS ymmetr.i.e.s. ..........2.9.2. .......1.3...W3.a .r.d.I .d.e.n.t.i.Rt.ei neosr,m alization,
11.5L ocaSly mmetrayn dI nteracTthieoonr. y.2 93 andG augeI nvaria.n.c.e. .......3.2.8. ...............
11.M6i nimaSlu bstitu.t.i.o.n. .......2.9.7. .......1.3...C4.h .a.n.g.ei.sn.t heT heorwyi trnha
I1 .7C haptSeurm mar.y. ............2.9.7. ...........I.n.s.t.eo.af.rnd . ..... ......................3.3.0. ................
B
13.S5h owintgh e inF ermioLno opE quals
11.8 AppenSdhioxw:i n[gQ ,S= ]0 . .......2.9.8. ........
theL inV erteCxo rrect.i.o.n. .....3.3.1. ..........
11.P9r oble.m.s. ................................................ 300
13.R6e -expres2snidnO gr deCro rrected
PropagatVoerrst,e axn,dE xternLailn e3s3 2
13.C7h aptSeurm mar.y. ............3.3.6. .....................
13.8P roble.m.s. ................3.3.7. ..............................
14.R enormalization:
PuttiIntAg l lT ogether 339
...........................
14.P0r elimin.a.r.i.e.s. ...........3.3.9. .........................
14.R1e normalizEaxtaimopnl e:
ComptonS'csa tte.r.i.n.g. ......3.4.0. ...............
d
14.R2e normali2zniOnrgd er
DivergeAnmtp litu.d.e.s. .......3.4.2. ...............
d
14.T3h eT otaAlm plitutdo2e n Orde.r. ...3.5.1. .....
14.R4e normaliztaotH iiognh eOrr ders:
OurA pproa.c.h. ............3.5.1. .......................
viii
14.H5i gheOrr der RenormaElxiazmaptlieo:n 17.S cattering 432
.................................................
ComptonS'csa tte.r.i.n.g. .........3...5..2.. .......
. 17.P0r elimin.a.r.i.e.s. ............4..3..2.. ...................
14.R6e normalinztihOn rgd er . .
DivergAemnptl itu.d.e.s. .....3.5..4. .....1.7..T.1h. e.C .ro.s.s. .S e.c.t...i.o.n.. .................3.4.2.. .......
14.T7h eT otaAlm plitutdone t Ohr de.r. ..3.6.4.. ... 17.R2e vieowfI nteracCtoinosne rvaLtaiwos4n 4 5
.
14.R8e normaliztaoAt liOlo rnd e.r.s. ....3. 6.4. ......1.7.A3n othLeoro ka tM acroscoCphiacr ged
. PartiIcnlteesr a.ct.i.n.g. ................ ..4.4.9. ...
14.C9h aptSeurm mar.y.. ..................3.6.5. .... . . .
. . ... . .. . 17.S4c atteirniQ nFTg: An InD eptLho o.k. ..54.2.
14.1Ap0p endiSxh:o winlgt enBtThe rm .
DropOsu t. .........................3.7.2. ......1.7...S5c. a.t.t.e.ir.ni. nQ gF STo:m eE xampl.e.s. .4.6.3. ...
14.1Pr1o ble.m.s. ................................3..7..3.. ... 17.B6r emsstraahnldu ng
.. . .. .. Infra-Drievde rge.n.c.es. ...........4..7..9.. .......
.
15R.e gularization 374 17.C7l osu.r.e. ..............4.8.2. ..................................
.........................................
15.P0r elimin.a.r.i.e.s... .....................3..7..4 . .....1.7...C8.h .a.ptSeurm mar.y. ..............4..8..2.. ...... ..........
15.R1e latiWoen'slN le e.d. ...................3..7..5.. . ....17.P9r oble.m.s... .....................................4.8.5. .......
15.F2i ndiPnhgo toSne lEfn ergFya ctor
Usintgh Ceu t-OMfeft hod. ......3.7.9. .........
..
15.P3a uli-ViRlelgaurlsa ri.z.a.t...i..o.n.. ....3..8.4. Addend.a. ..................4.8.7. ..................................
. . .
15.D4i mensioRneaglu lari.z.at...i..o..n.. ..3.8.5. ....1.8.P. a thIn tegrianQl usa ntuTmh eorie4s8:8
15.C5o mpariVnagr ioRuesg ularization ...
Approac.h.e.s. .....................3...8...8... .... ...1.8.P0r elimin.a.r.i.e...s.. ..............4.8.8. ...................
.. .
15.F6i ndiPnhgo toSne lEfn ergFya ctor 181.B ackground Math:
UsinDgi mensioRneaglu lariz.a..t.i3.o8.n8. ExamplaensdD efinit.i.o.n.s. ......4..8. 8. ........
.
15.F7i nditnhgVe e rtCeoxr rectFiaocnt or 18.D2i fferKeinntdo sfI ntegration
UsinDgi mensioRneaglu lariz.a..t..i3o9n3 witFhu nctio.n.a.l..s.. .........................4...8.. 9
. . .
15.F8i ndiFnegr miSoenl Efn ergFya ctor 18.T3h eT ransiAtmipolni t.u.de.. ............4..9.0. .....
UsinDgi mensioRneaglu lariz.a.t.i3.o9.n7. .. 18.E4x presstihnWega veF unctiPoena k
15.C9h aptSeurm mar.y. ..............3..9..7.. ....... .....i.nT ermosf t hLea grang.i.a.n... ......4..9.2. ....
..
15.1Ap0p endAidxd:i tioNnoatleo sn I nteg3ra9l9s 18.F5e ynmanP'astI hn tegArpaplr oach:
TheC entral. .I.de.a. ............4..9..3.. ...........
15.11P roble.m.s. ...........................4..0..0. .......... . ..
. . . . 18.S6u perimpoasF iinngiN tuem beorf P at.h4.s9 4
18.S7u mmaroyfA pproac.h.e.s. .......94.7 ...............
18.F8i niStuem st oF unctioInnatle g.r..a.l.s4. 9.8. ..
.
ParFto urA:p plicattioEo xnp eirment. 401 18.A9n ExamplFer:e Pea rti.c.l.e. ....5.0.2. .............
•.•.•.
18.1QFT0 viPaa tIhn teg.r.al..s.. .............5.0.6.. ..
. . .
16P.o stdicotfiH oins torical 18.11C haptSeurm mar.y. ...................5...0...9
.. .... ...
ExperimenRteaslu l....t....s.... .................. 402 18.1Ap2p end.i.x. ........................5.0.9. ................
. . .
16.P0r elimin.a.r.i.e.s. ......................4...0 ..2.. .....1.8...1P.3r.o bl..e.m. .........................................5.0.9. ...
16.C1o ulomPbo tentiinRa QlM ............4..0..2.. ...
. 19L.o oking BackawnadLr odo kinFgo rward:
16.C2o ulomb PotienQn FtTi. a.l. .........4..0..4.. .....
. Book SummaarnydW hat's Next5 10
16.O3t hePro tentainadBl oss oTny pe.s. ....4.1.0. ..........
16.A4n omalous Magneti.c ...M..o...m.e.4n.1t.1 . .... 19.P0r elimin.a...r...i..e.s. .......................5..1 .0. .......
16.T5h eL ambS hi.f.t.. ............................4. .2..7. . 19.B1o okS ummar.y. ..................................5.1.1. ...
16.A6 N otoen Q ED S.ucceOsvs.eerRsQ .M .. ..4.2.7. 19.W2h at'Nse x.t. .............................5.1.9. ............
16.C7h aptSeurm mar.y. ....................4..2..8.. .... .
. . . .
16.P8r oble.m.s. ................................4..3..0.. ...I.n.d.e....x..... ........... ............................... ................ 521
Tabloef W holeneCshsa rts
Preparation
10-C1o mpariosfoVn a cuumF luctuation
1-1T heO veraSltlr uctoufPr hey sics ....5. ...............
Scenar.i.o.s. .............2..7.8. ............................
1-2C ompariosfoT nh reTeh eori.e.s. ......7. .............
10-D2i scrvestC eo ntinuVoeurss ioonfQs Ff .2 81
2-1C onversiboentsw eNeant urHaylb,r id,
11-T1y peosf T ransforma.t.i.o.n.s. ...2.9.3. .............
andc gsN umeriQcu antit.i.e.s. ....1.4. ...........
11-S2u mmaroyf G lobaanld L ocaIln ternal
2-2S ummaroyf C lassi(cVaalr iational)
SymmetfroyrC andC o. ..........2.9.5. ........
Mechani.c.s. ..............2.0. .................................
11-3S ummaroyf S ymmetErfyf ects
2-4S chrodivnsgH eeri senbPeircgt ure
forI nterac.t.i.o.n.s. ........2.9.8. .......................
EquatioofnM so tio.n. ..........2.8. ...................
2-5S ummaroyf Q uantum Mechanics ParTth reeR:e normalization
(Heisenberg .P.i.c.t.u.r.e.). ...3.0. ..................
14-T1w oR outetsoR enormaliz.a.t.i.o.n.3 .5.0. ......
ParOtn e:F reeF ields 14-T2y peosf F eynman Diagrams .3.5.3. ................
3-1B osonvssF ermio.n.s. ...........6.5. .......1.4.-.C3.o .m.p.a.r.iC.ne.gr. t.a.Ti.yn p eosf
FeynmaDni agra.m.s. .........3.5.4. ..................
3-2P hysicHaill,b earntdF, o ckS pac.e.s. ...6.8. .......
14-4 RenormalSitzeapttsoi2 onndO rdeirn a .3 68
3-3Q uantuHma rmonOiscc illator
ComparteodQ Ff FreSet at.e.s. ....6.9. .......1.4.- R5e normalizSatteiptosonn thO rde.r. ..3.6.8. ...
3-4D ifferKeinntdo sfO perationrQ sF f. ...7.9. ..... 15-1 Wick Rotatio.n. .S.u.m.m.a.r.y.3 .7.7. ..............
4-1S piY2n PartiScplieSn u mmar.y. .....1.0.2. .......1.5.- C2o mpariosfoF no uRre gularization
Techniq.u.e.s. ............3.9.7. ...........................
5-1S ummaroyf C lassiEclaelc tromagnetism
PotentTihaelo r.y. ...........1.4.1. .....................
ParFto urA:p plicattioEo xnp eriment
5-2C ompariSnpgi naonrd P olarization
16-B1o soSnp iann dL ikCeh arg.e.s. ......41.1 .........
BasiSst at.e.s. .............1.4.6. .........................
16-T2h eoretaincdEa xlp erimeVnatlaule. s. .4.1.2. .
5-3G upta-BleWuelaekLr o renCtozn dition
17- 1S ummaroyf D efinitainodn s
Overvi.e.w. ..............1.5.4. ............................
Interpretoafcrt aionndds cr ldD. 444
5-4Q FfO verviePwa,r1 t:F romF ielEdq uations ..............
17- 1S ummaroyf D efinitainodn s
toP ropagaatnodrO sb servab.l.e.s. .1.5.6. .....
Interpretoafcrt ainodnd scr ldQ 444
6-1S ymmetrSyum mar.y. ...........1.6.6. ................... ..............
17-S2c atteOrfifnS gt atioTnaarrgyfe otr
6-2G alilvesaL no renTtrza nsforma.t.i.o.1n.6s.8 . ..
Different Physical Theo4r4i5e s ....................
6-3S ummaroyf E ffeocftL orentz
17-T3w oP artiEcllaes tCiocl lisions
TransformoantF iioenl .d.s. ......1.7.2. ...........
(Non-relat.i.v.i.s.t.i.c.). ....4.5.0. ....................
6-4W ayst oD etermiinfae Q uantity
17-T4w oP article CEollalsitsiico ns
isC onserv.e.d. ............1.7.7. .........................
(Relativ.i.s.t.i.c.). ........4.5.1. .........................
ParTtw o:I nteracFtiienlgd s 17- 5F ermioSnp iSnu mR elati.o.n.s. ...4.6.0. ..........
7-1C ompariSncgh rCidinHgeeirs,e nberg, 17- 6D iffereCnrtoisaSsle ction
andI nteracPtiicotnu. r.e.s. ......1.8.8. ..........D.e.t.e rminaitnQi Ffo n. .........4.8.3. ...............
7-2E xamplferso tmh eT hrePei ctures .1.9.3. ..........
Addenda
8-1 Keeping FourS-imgonSmste rnatia.g .h.2t.3 .4.
18-S1o meW ayst oI ntegrFautnec tio.n.a.l..s4. 90. .
8-2C omparing TPyepritcuarlb aTthieoonr y
18-E2q uivalAepnptr oacthoe s
toQ ED 238
................................................... Non-relatiQvuiasnttiuMcme chani.c.s4. 9.8.
8-3S ummaroyf V irtuPahlo toPnr operties
18-A3d dinPgh asoartts h eF inaElv ent
fo1r DA ttracatnidoR ne puls.i.o.n. .2.4.6. ....
foTrh reDei scrPeatteh .s. .........4.9.9. ...........
8-4Q Ff OverviePwa,r2 t:F romO perators
18-C4o mparing PTahretoirctylo e
andP ropagattooF resy nmaRnu le.s. .2.4.8. ..
FielTdh eorCyl:a ssiacnadQl u antu.m.5 .0.6
9-1L oopC orrect.i.o.n.s. .........2.6.5. .......................
18-C5o mpariNnRgQ M toQ Ff fotrh e
ManyP athAsp proa.c.h. .......5.0.8. ...............
18-6S upeSri mple Sum.m.a.r.y. .....5.0.8. ..............