Mue luc. .

Li1i n6i dAu

Chu'dng 1. V~t ly hl;lt cd ban

1.1. Cac ky hi~u (Conventions) . . . . . . . . . . . . . . . . .

1.2.D5itu<;IngnghiencUu """""" '..1.3. Phanlo~icaeh~tcdbll.ll......................

1.4. S5 fermion va quy t1k lQc !Ita (Fermion number and selectionrules) ................................

1.5. D5i xang unita - SU(2) .............

1.6. Nh6mSU(2) """"""""'"

1.7. Nh6mbi~nd6iSU(2) .......................

1.8. Cacdatuy~n (Multiplets) . . . . . . . . . . . . . . . . . . . . .

1.9. Cac phan da tuy~n (Antimultiplets) ...........1.l0.Cacdatuy~nSU(2) ....................

1.11.Nh6mU(I) ....................

1.12.D5ixangSU(3)..................

1.13. Bi~u di~n cd sa ta = ~: cac quark. . . . . . . . . . . . . . . .1.14. Bang Young (Young tableaux) ..................

1.14.1. Khai tri~n tfch cae bi~u di~n thanh t6ng . . . . . . . . .1.14.2. Bang Young cho bi~u di~n lien h<;lp(Conjugate represen-

tations) ...........................

1.15.Phan tich cii.cda tuy~n (Decomposition of multiplets) SU(M)@SU(N)ESU(M+N) .......................

1.16. Nhan cac da tuy~n c6 tich U(I)x """"""""

1.17. ta = Fa, (Fa)bc = -ifabc Bi~udi~n chinh quy - bat tuy~n . . .1.18.L\lctuy~n(Sextet) .........................

1

3

3

3

4

7

11

12

13

13

14

14

22

24

25

26

31

33

35

40

42

47

iv Mr,lCl~c

1.19.Cong thUckh6i htQngGell-Mann- Okubo. . . . . . . . 49

Chttdng 2. Hlnh thuc lu(in Lagrange 51

2.1. Cd hQc c6 di~n va hinh thuc lu~n Hamilton. . . . . . . . . .. 51

2.2. Hinh thuc lu~ Lagrange trong chuy~n dQng cua hl,\t . . . . .. 532.3. Cd hQc htQng tu tUdng d6i tinh (Relativistic Quantum Mechanics) 55

2.3.1. 1oi gil\i cua phudng trinh Dirac. . . . . . . . . . . . .. 582.3.2.Phanhl,\t 64

2.3.3. ChuAn boa va cae hE:!thUc tn,tc giao 66

2.4. Phudng trinh Euler - Lagrange. . . . . . . . . . . . . . . . .. 692.5.DjnhlyNoether's 702.6. 1ythuy~ttrUbngc6di~n 72

2.6.1. 1y thuy~t c6 di~n roo truong vo huffilgthl,tc. . . . . .. 732.6.2. Ly thuy~t c6 di~n cho trubng vo huffilg phuc . . . . . .. 78

2.7. Truong vo hudng thl,tc (luQngtu) . . . . . . . . . . . . . . . .. 80

2.8. Truong vo hudng phuc (luQngtu) . . . . . . . . . . . . . . . .. 822.9.Truongspinor 832.10.Truong spinor khong kh6i luQng. . . . . . . . . . . . . . . . .. 872.11.SpinorWeylvaMajorana 89

2.12.Ra beta hai liln khong co neutrino (Neutrinolessdouble (3decay) 932.13.Ma tr~ kh6i luQngcua neutrino. . . . . . . . . . . . . . . .. 932.14.Di thUbngtr\lc (Axial anomaly) . . . . . . . . . . . . . . . . .. 952.15.Truong vector co kh6i luQng . . . . . . . . . . . . . . . . . . .. 95

2.16.Truong chuAnvector (Massivevector gauge boson) . . . . . .. 982.17.Vectorphancl,tc 100

2.18.Truong vector khong kh6i luQng(Masslessvector field)-Truongdi~nti:t 103

2.19.PhudngtrinhMaxwell 1O6

2.20.Hi~uling Aharonov-Bohm(AB effect) . . . . . . . . . . . . .. 1082.21.Cac d6i xling trong ly thuy~t trubng luQngtu . . . .. . . . .. 110

2.21.1. Nhom d6i xling ngoai - nh6m Poincare. . . . . . . . .. 1102.21.2.Cacbi~udi~nunita 1132.21.3.Nh6md6ixlingtrong 116

Chttdng 3. Ma tr(in tan x~ (8 matrix) 121

.3.1. Phudn&phap Mc vo (Peelingmethod) - cach xay dl,tngphfuIdlnh1283.2. Cae qua trinh trong truong ngoai.(Processesin External fields) 134

.

M,!,c l,!,c v

3.3. Quy tlk Feynman (Feynmanrules) . . . . . . . . . . . . . . .. 1363.4. H~ s5 d5i xUngcua gilm d6 (Symmetry factor) S . . . . . . .. 1393.5. Ti~tdi~ntanx~ 1423.6. Tan~e+e--+J1.+J1.- 1453.7. Tan~e+e--+e+e 149

3.8. Cac th~ nang kinh di~n (ClassicalPotentials) """'" 1503.9. Sl1huyc~p e+e--+, 1553.10.Buc x~ ham (Bremsstrahlung). . . . . . . . . . . . . . . . . .. 1563.11.H~t kh6ng b~n (Unstable particles) 158

3.11.1. Dinh ly quang hQc(Optical Theorem) . . . . . . . . .. 1583.11.2.H~tkh6ngb~n 160

3.12. Quy tlk Feynman cho cae ly thuy~t kh6ng baa toan s5 fermion 1603.13.D6ng nhfit thuc Fierz (Fierz identities) . . . . . . . . . . . . .. 1623.14.DinhlyCPT(CPTtheorem) 164

Chudng 4. Phiin kyvaphudng phap chinh thu nguyen 175

4.1. Ky dj trong lythuy~t trubng (Singularities in QFT) 1754.2. ThU nguyen chinh tlk (Canonical dimension) . . . . . . . . .. 1784.3. Gian d6 phan Cl1cchan kh6ng (Vacuumpolarization) . . . . .. 1794.4. Phuong phap chinh thu nguyen (Dimensionalregularization) . 1804.5. Phan kYMng ngo~i (IR divergence) . . . . . . . . . . . . . .. 1894.6. Phuong phap chinh Pauli - Villars. . . . . . . . . . . . . . .. 1934.7. B~cphan ky cua gian d5 (Superficialdegree of divergence) .. 1984.8. Phan lo~i cae ly thuy~t till chuAnboa (Classificationof theories

byrenormalization) 2054.9. B~ phan ky trong kh6ng gian D chi~u . . . . . . . . . . . . .. 206

Chudng 5. Ly thuyi!t tai chuAn boa (Renormalization theory) 2095.1. Tai chuAnboa kh5i luc;1ngva ham s6ng . . . . . . . . . . . . .. 2095.2. TillchuAnhoalythuy~ttp4 2165.3. Ly thuy~t cp4trong gan dung hai vang . . . . . . . . . . . . .. 225

5.3.1. H8.mGreenhaidi~m 225

5.3.2. Bien d(>tan Xq.M(pIP2 -+ P3P4) .. . . . . . . . . . .. 2295.3.3. Gian d6 lien k~t y~u va. till chuAnhoa (Reducible dia-

grams and renormalization) . . . . . . . . . . . . . . .. 2395.4. Tai chuAnh6a trong QED (Renormalization in QED) 241

vi M'l,LC l'l,Lc

Chttdng 6. Nh6m tai chuAn boA (Renormalization group) 2516.1. Phl1dngtrinh nh6mtai chuAnhoa-Phl1dngtrinh Calhin-Symanzik

252

6.2. Tfnh ham beta va gamma (Calculation of (3and, functions) . 2536.3. Giai phl1dngtrlnh Callan-Symanzik. . . . . . . . . . . . . . .. 258

Chttdng 1. Ly thuy~t trttClng chuAn (Gauge theory) 2657.1.Nh6mLie 265

7.2. Trl1dng chuAn cho cae da tuy~~ d~ng c(>t . . . . . . . . . . . .. 266

7.3. Ll1angtensd (Dualtensor) . . . . . . . . . . . . . . . . . . . .. 271

7.4. Trl1bngchu1\.ncho cac bi~u dii'!ncrunh quy/ph6 (Regular repre-sentation) 272

7.5. Ly thuy~t tl1dngd6i r(>ngnhl1la.ly thuy~t trl1bngchuAn(Gaugetheoryof generalrelativity) . . . . . . . . . . . . . . . . . . .. 274

7.6. Lythuy~tgaugeO(n) 2767.7. Lythuy~tth6ngnh~tWn(GUT)SU(5) . . . . . . . . . . . .. 2787.8. Ll1c;1I1gtl't hoa trl1dng chuAn (Quantization of gauge field) ... 282

7.9. Phi\. va d6i xling tv phi\.t va. cd ch~ Higgs (Higgs mechanism) . 287

7.10. Chu1\.nunit a (Unitary gauge) . . . . . . . . . . . . . . . . . .. 290

7.11.ChuAnR~(R{gauge) ~917.12. M(>ts6 ki~u pM va d6i xling khac , 293

7.13.Ly thuy~t siEjuclan (Superconductivity) 295

7.14.D6ngnh~tthUcWard-Takahashi .298

Chttdng 8. MAu Glashow-Weinberg-Salam 3058.1. Tl1dngtac y~u trl1(Jckhi c6 ly thuy~t chuAn . . . . . . . . . .. 3058.2. Nhl1ngnguyEjntAcxliy d1,tngcac s6 h~g tl1dngtae (Rules for

coupling construction) 3078.3. Mo hlnh Glashow-Weinberg-SalamSU(2)L x U(l)yw 3098.4. Cae s6 h~g ma FP (FP ghost terms) 3268.5. Cd cM GIM va.quark duyEjn(GIM mechanism and Cquark) .. 3378.6. CKMmatrix 3398.7.,Racuaca.cbosonWvaZ 342

8.7.1. RacuabosonW 3428.7.2. RacuabosonZ 344

8.8. Di thl1bng tr\lc (Axial anomaly) . . . . . . . . . . . . . . . . .. 345

8.9. Neutrino phan cvc phlii (Right-handedneutrino) . . . . . . .. 350

M'(LC l'(Lc vii

8.10. Tinh tal chuAn boa va ti~t di(jn t~ x1;t(Renormalizability and

cross-section) 350

8.11. Bi~n d6i 0, P, T trong cae ma hlnh chuAn . . . . . . . . . . .. 352

8.11.1. Phep nghjch dao khang gian (Pari&y) 3528.11.2.LienhQpdi(jntfch 354

8.11.3.Nghjchdaothoigian 356

8.11.4. DjnhlyCPT 361

8.12. Lagrangian toan phfin (Full Lagrangian) . . . . . . . . . . . .. 364

8.13.811 tal chuAn boa cua ma hlnh GW8 va cac ma hlnh ma rQng . 368

Chudng 9. Hiil!u dinh tudng tac ml;Ulh m9t yang (QCD correc-

tions) 3719.1. Hamdinh ,' 372

9.2. N1!.nghlQngrieng cua quark. . . . . . . . . . . . . . . . . . .. 3799.3. Tai chuAnboa kh6i h1Qngva ham s6ng . . . . . . . . . . . . .. 380

9.3.1. Thua s6 d1;tngtai chdn hoa . . . . . . . . . . . . . . .. 3819.3.2. H(jqua.quail trQngcua tai chuAnhoa kh6i luQng . . .. 382

9.4. D6ng g6p cua gluon a.o(Virtual gluon contribution) 3839.5. D6ng g6p cua gluon th~t (Real gluon contribution) . . . . . .. 3849.6. K~t qua.cu6i cling va nh~n xet . . . . . . . . . . . . . . . . .. 386

Chudng lO.Phudng trlnh nh6m t8.i cllUAn boa trong ly thuy~tchuAn non-Abelian 389

10.1.Ham beta trong QED ({3function in QED) . . .. 3891O.1.1.Phancl,tcchankhOng 39110.1.2. Tai chuAnhoa ham dinh . . . . . . . . . . . . . . . . .. 391

10.2. Phudng trlnh Callan - 8ymanzik (II) . . . . . . . . . . . . . .. 394

10.2.1. Tfnh ham {3va , (Calculation of (3and, functions) .. 39510.3.Ham {3trong QCD ({3function in QCD) . . . . . . . . . . . .. 396

10.3.1. 86 h1;tngpha.nnang luQngrieng cua quark Zq . . . . .. 39610.3.2. 86 }w.ngphan cua dinh quark-gluon Zl 39710.3.3. 86 h1;tngphan cua n1!.ngluQngrieng cua gluon . . . . .. 39910.3.4. HAngs6 ch1;tytrong QCD . . . . . . . . . . . . . . . .. 40110.3.5. Ham {3trong ly thuy~t th6ng nh~t tudng tac ({3functions

in unified theories) 402

Chudng 11.St! chuy~n boa ctia neutrino (Neutrino oscillation) 411

viii M'I,£cl'l,£c

11.1.Matr~ khOih:tc;lngcuaneutrino. . . . . . . . . . . . . . . .. 41111.2.811chuy~nhoa cua neutrino (Neutrino oscillation) 41211.3.Hlnh th~c lu~ Hamilton cho sll chuy~nhoa neutrino. . . . .. 418

11.3.1. 811chuy~nhoa neutrino m~t trClitrong roAnkhOng . .. 41811.3.2. 811chuy~nhoa neutrino trong moi trubng dOngnMt .. 42111.3.3. 811chuy~nhoa trong moi tn:tbngkhOngd6ng nMt . .. 427

11.4.un giiLibi~n d6i phi dQtxuAt (Adiabatic) . . . . . . . . . . .. 427

11.5. Cae hi<!u~g dQt xuAt (Nonadiabatic effects) . . . . . . . . .. 429

11.5.1. ThamsOphidQtxuAt 43111.5.2. Danh gia xac BoAtnMy . . . . . . . . . . . . . . . . .. 43311.5.3.T6mtlitICligiiLi 436

11.6.Chuy~ndQngclla neutrino trong tu trubng. . . . . . . . . . .. 43711.6.1. 8Vchuy~nboa neutrino trong tu truClng . . . . . . . .. 439

11.6.2.Danhgiamomenttu 441

Chudng 12.8ieu dAi xUng (8upersymmetry) 44312.1.8ieukhOnggian 44412.2.8ieutruClng 44612.3.Bi~nd6i sieu d6i x~g (SUSYtransformations) . . . . . . . .. 44712.4.8ieu trubng chiral, pUn chiral va vector. . . . . . . . . . .. 44812.5.LagrangianvataedQng 45112.6.MOhlnh chuan sieu d6i x~g tOithi~u (MSSM) . . . . . . . .. 455

Ph~ l~c A.Ky hi~u va dinh nghia 459

Ph\}.l\}.cB. Ly thuy~t di~n y~u 80(3) 463B.1.Vituvadatuy~n 463B.2.Lythuy~tdii;ny~u80(3) 465

Ph\}. l\}.c C. Cach x8y d1!llg bAt bi~n qua bang Young trong mAu3-3-1 469

Ph\}.l\}.c D. Tinh e+e- J.L+J.L-theo diM ly Wick 473

Ph\}. l\}.cE. Cac cOng thuc tich phiin vo:ng 481

E.O.1. Caehamlogarit 486

E.O.2. Caeham8pence 486

E.1. TichphAnvoiba, bOnhamtruy~n . . . . . . . . . . . . . . .. 487

Mv-clv-c ix

F.1. Cac hfu1gs6 v~t 1:5'va c6ng thuGchuy~nd6i . . .. . . . . . .. 506

PhI}.ll}.cG. Ti~t di~n tan ~ va phiin ct1c cua cac h~t ngoiU 509

PhI}. ll}.c H. Vi~c giai thich tinh ct1c nha cua khOi h.t<;1ngneutrino 513

H.O.1. C<1ch~ see-saw (See-saw mechanism) . . . . . . . . . .. 513

H.0.2. C<1ch~ b6 dfnh (Radiative mechanism). . . . . . . . .. 515

PhI}. ll}.cI. Ham (3 trong cac mo hinh 3-3-1 ((3 functions in 3-3-1models) 5171.1. T6ngquanv~m6hlnh 517

1.1.1. M6 hinh 3-3-1model with neutrino phan e1,tephil.i . .. 5171.1.2. M6hinh3-3-1ti~tki1:m 5181.1.3. M6 hinh 3- 3-1 t6i thi~u . . . . . . . . . . . . . . . . .. 518

1.1.4. Cac m6 hinh 3-3-1sieu d6i x1'tng . . . . . . . . . . . .. 5191.2. Cae ham beta 519

1.2.1. Ham beta trong ma hlnh vdi neutrino phan e1,tephil.i .. 5201.2.2. Ham beta trong ma hinh 3-3-1ti~t ki1:m. . . . . . . .. 5221.2.3. Ham beta trong ma hinh 3-3-1t6i thi~u . . . . . . . .. 522

1.3. Ham beta trong cae ma hinh 3-3-1sieu d6i x1'tng . . . . . . .. 5241.3.1. Ham beta trong ma hinh 3-3-1 vdi neutrino phan e1,te

phaisieud6ix1'tng 5241.3.2. Ham beta trong ma hinh 3-3-1 ti~t ki1:msieu d6i x1'tng. 5261.3.3. Ham beta trong ma hinh 3-3-1t6i thi~u sieu d6i x1'tng . 527

1.4. HAngs6 tl1<1ngtae ehuiin boa t6t . . . . . . . . . . . . . . . .. 528

PhI}. ll}.c J. Quy tiie Feynman cho mAu Glashow - Weinberg -Salam 533

J.1. Quy tAc Feynman trong ehuiin R~ """""""" 533J.2. Thua s6 nh6m d6i x1'tngtrong 545