,,..,. 1

016 9 3 6

0 016 1 0 1 10 1 1 17 1..,,..,. 1

1 c = h = G = ε 0 = 1. 1.1 L L T V 1.1. T, V. d dt L q i L q i = 0 1.. q i t L q i, q i, t L ϕ, ϕ, x µ x µ 1.3. ϕ x µ, L. S, L, L S = Ld 4 x 1.4 = Ld 3 xdt 1.5 = Ldt 1.6

... x µ L L ϕ ϕ x µ = 0 1.7 1..,, A µ x µ ν A ν x = j µ x 1.8 µ µ = t 1.9 µ x µ 1.10 µ x µ 1.11. 4 A µ x 4 j µ x A µ x = ϕx, Ax 1.1 j µ x = ρx, jx 1.13, ϕ, A.. L = 1 4 µa ν x ν A µ x µ A ν x ν A µ x A µ xj µ x 1.14 3

1.3 1/ iγ µ µ m ψx = 0 1.15. γ µ, ψx. L = ψx iγ µ µ m ψx 1.16., ψx ψx. ψx = ψx γ 0 1.17 1.4, H = 1 m p 1.18., m, p.. F = eq E + v B 1.19, e, Q 1, +1. E, B, v. H H H eqϕ 1.0 p p eq A 1.1 H = 1 p eqa + eqϕ 1. m 4

. 1.1,, i µ i eqa µ 1.3 = i µ + ieqa µ 1.4. 1.16,,, QED L = ψx iγ µ + ieqa µ x m ψx 1 4 µa ν x ν A µ x µ A ν x ν A µ x 1.5.. 1, ψxiγ µ ieqa µ xψx = ψxγ µ eqa µ xψx 1.6. D µ F µν, 1.5 D µ ϕx µ + ieqa µ x ψx 1.7 F µν x µ A ν x ν A µ x 1.8 L = ψx iγ µ D µ m ψx 1 4 F µνxf νµ x 1.9. F µν E B. F µν = 0 E x E y E z E x 0 B z B y E y B z 0 B x E z B y B x 0 1.30 5

.1 U1 U1. ψx ψ x = e iqθx ψx.1 A µ x A µx = A µ x 1 e µθx. ψ= ψ γ 0 D µ. ψx ψ x = ψxe iqθx.3 D µ ψx D µψ x.4 = µ + ieqa µx ψ x.5 [ = µ + ieq A µ x 1 ] e µθx e iqθx ψx.6 = µ e iqθx ψx +ieq A µ x 1 e µθx e iqθx ψx.7 = e iqθx iq µ θxψx + µ ψx +e iqθx ieqa µ x ieq e µθx ψx.8 = e iqθx µ ψx + ieqa µ x.9 = e iqθx D µ ψx.10 QED 1.9 U1.. ψx iγ µ D µ m ψx ψ x iγ µ D µ m ψ x.11 6

= ψxe iqθx e iqθx iγ µ D µ m ψx.1 = ψx iγ µ D µ m ψx.13 F µν x F µν.14 = µ A νx ν A µx.15 = µ [A ν x 1 ] [ e νθx ν A µ x 1 ] e µθx.16 = µ A ν x ν A µ x 1 e µ ν ν µ θx.17 = µ A ν x ν A µ x.18 = F µν.19.,.,. µ ψx, µ ψx µ ψ x.0 = µ e iqθx ψx.1 = e iqθx µ ψx + iqe iqθx ψx µ θx., U1, A µ ψγ µ eqa µ ψ.. U1 : SU : SU3 : 7

.3 A µ 1/m AA µ A µ., 1 m AA µ A µ 1 m AA µa µ.3 = 1 m A A µ 1 e µθ A µ 1 e µ θ.4 = 1 [ m A A µ A µ 1 e A µ µ θ + A µ µ θ + 1 ] e µθ µ θ.5 1 m AA µ A µ.6,. m A = 0.. 8

3.,,. 1,.. 3.1 ϕx. L = µ ϕ µ ϕ + µ ϕ ϕ λ ϕ ϕ 3.1 1.1, 1 T, 3 V., 3. U1. ϕx ϕ x = e iθ ϕx 3. ϕ x ϕ x = e iθ ϕ x 3.3 θ x,. ϕ xϕx = ϕx 3.4, V V = µ ϕ + λ ϕ = λ ϕ µ µ4 λ 4λ 3.5 9

. V. λ < 0, ϕ, λ ϕ,. λ > 0. V ϕ = µ ϕ + λ ϕ ϕ 3.6, V ϕ = 0 ϕ = µ /λ. µ < 0, ϕ = 0 V. µ > 0, ϕ = µ /λ V. ϕ = µ /λ, ϕ,.. µ < 0, µ > 0. µ.. vaccum expectation value, vev 0 ϕ 0 v 0 ϕ 0 = µ λ = v 3.7, 1,. v ρx πx ϕx = 1 v + ρx exp i πx v. U1 3.8 ρx ρ x = ρx 3.9 πx π x = πx + θv 3.10, U1. v ρx πx ϕx = 1 v + ρx + iπx 3.11 10

, 3.1 L = 1 µπ µ π + 1 µ ρ µ ρ µ ρ µ λρ ρ + π λ ρ + π + const. 3.1 4., µ ρ = m ρρ 3.13, ρ m ρ = µ. π m π = 0. π NG. 3. L = D µ ϕ D µ ϕ + µ ϕ λ ϕ 4 1 4 F µνf µν 3.14., D µ, ϕ q = Qe, D µ = µ + iqa µ 3.15, F µν 1.8. µ > 0, λ > 0, v = µ /λ ϕ = 1 v + ρ exp i π v 3.16, 3.14 L = 1 µ ρ µ ρ µ ρ µ λρ 3 λ 4 ρ4 + 1 qv 1 + ρ A µ + 1 v qv µπ A µ + 1 qv µ π 1 4 F µνf µν + const. 3.17 11

., NG π. V µ A µ + 1 qv µπ 3.18 1 qv 1 + ρ A µ + 1 v qv µπ A µ + 1 qv µ π = 1 qv 1 + ρ Vµ V µ v 3.19, 1/m V V µ V µ, V µ m V = qv, ρ m ρ = µ = λv., A µ NG π,..,. π A µ q = 0 q 0 ρ m ρ = µ ρ m ρ = µ } m π = 0 1, NG m A = 0 V µ m V = qv 3 1

4 4.1. n p + e + ν e β µ ν µ + e + ν e π ud µ + ν µ. 4. L 4 fermion = G J µj µ 4.1, G,, G = 1.1663786 10 5 GeV = 1.03 10 5 m proton 4.. J µ,,. J µ = J lepton µ + J quark µ 4.3 ψ e, ψ νe e, ν e,, J lepton µ = eγ µ 1 γ 5 ν e + µγ µ 1 γ 5 ν µ + τγ µ 1 γ 5 ν τ 4.4. γ 5, γ 5 iγ 0 γ 1 γ γ 3 4.5 13

, γ 5 = iγ 0 γ 1 γ γ 3 = γ 5 4.6 γ 5 = γ 5 4.7 γ µ γ 5 = γ 5 γ µ 4.8 γ 5 γ µ = γ µ γ 5 4.9., ψγ µ ψ vector, ψγ 5 γ µ ψ axial vector., V A. 4. γ 5 1 P L ψ L P L ψ = 1 γ 5 ψ 4.10., γ 5 +1 P R ψ R P R ψ = 1 + γ 5 ψ 4.11., 1 1 γ 5 = 4.1 +1 +1 +1 P L = 1 γ 5 +1 = 4.13 0 0 0 P R = 1 + γ 5 0 = 4.14 +1 +1 14

,.. P L = P L 4.15 P L = P L 4.16 P L P R = 0 4.17 4.3 SU L e νel νe L e = P L e e L 4.18.,. L e, J electron µ = eγ µ 1 γ 5 ν e 4.19 = eγ µ P L ν e 4.0 = e L γ µ ν el 4.1 = 0 0 νel ν el e L 4. 1 0 e L 0 0 = L e L e 4.3 1 0. σ 1 = σ = σ 3 = 0 1 1 0 0 i i 0 1 0 0 1 4.4 4.5 4.6 15

,. 0 0 1 0 = σ1 iσ 4.7 jµ a = σ a L k γ ν k=e,µ,τ L k a = 1,, 3 4.8, Jµ lepton = jµ 1 ijµ j 1 i Jµ lepton = j 1 µ + ij µ = j 1 µ + ij µ µ 4.9 = j 1+i µ 4.30. SU 1 i. Jµ quark, J µ SU. SU, T a a = 1,, 3, T. SU SU W W weak isospin SU L L left handed. L e = νel e L Q T 3 0 + 1 1 1 L e SU L, Q T 3, U1 EM SU L.,. SU L U1 Y, weak hyper charge Y. L e, L µ, L τ Y = 1 Q = T 3 + Y 4.31. 16

SU L U1 Y U1 EM T a Y Q = T 3 + Y 4.4 SU L A µ = A 1 µ, A µ, A 3 µ = a=1,,3, g. U1 Y B µ, g. L gauge = 1 4 µ Aµ ν Aµ g A µ A ν A g µ 4.3 1 4 µb ν ν B µ 4.33., A µ A ν = a,b,c ε abc A b µa c ν 4.34, SU. Φ = ϕ1 ϕ 4.35., ϕ 1 ϕ, 4. 0 Φ 0 = 1 0 v 4.36. v 0, Q = 0, Y = +1., ϕ 1 Q = T 3 + Y/ = +1/ + 1/ = +1, ϕ Q = T 3 + Y/ = 1/ + 1/ = 0. 17

Φ D µ Φ = µ I + ig 1 IB µ + ig 1 A µ τ Φ 4.37., I, τ i,. A µ τ = A 1 µτ 1 + A µτ + A 3 µτ 3 4.38 Φx Φ x = e iθx Φx 4.39 U1 Y B µ x B µx = B µ x g µθx 4.40. SU L Φx Φ x = UxΦx = exp i τ θx Φx 4.41 A µ x τ A µx τ = Ux A µ x τu x i g Ux µu x 4.4. L Higgs = D µ Φ D µ Φ + µ Φ Φ λ Φ Φ 4.43., v = µ /λ Φx = exp i χx τ v. U 1 = exp i χx v τ, Φ = UΦ = 1 1 0 v + ϕx 0 v + ϕx 4.44 4.45 18

, Φ χ. 4.43 = 1 L Higgs + µ µi + i ga3 µ + g B µ g A 1 µ ia µ g A 1 µ + ia µ ga 3 µ + g B µ 0 v + ϕx v + ϕ λ 4 v + ϕ 4.46 = 1 0 + i g A 1 µ ia µ v + ϕx µ ϕx ga 3 µ + g B µ + µ v + ϕ λ 4 v + ϕ 4.47 = 1 µϕ + 1 [ A 8 g 1 ] µ + A µ v + ϕ + 1 8., ga 3 µ g B µ v + ϕ + µ v + ϕ λ 4 v + ϕ4 4.48 Zµ W µ 1 A 1 µ ia µ 4.49 W µ = 1 A 1 µ + ia µ 4.50 4.51 A µ 1 g + g g g g g A 3 µ B µ = cos θw sin θ W A 3 µ sin θ W cos θ W B µ 4.5 cos θ W = g g + g 4.53 sin θ W = g g + g 4.54 M W = 1 gv 4.55 M Z = 1 g + g gv = M W 4.56 cos θ W M H = µ = λv 4.57. θ W. 19

W µ W +, W µ W, Z µ Z 0, A µ, ϕ., 4.48 L Higgs = 1 µϕ +MW W µw µ 1 + ϕ v + 1 M ZZ µ Z µ 1 + ϕ v + µ v + ϕ λ 4 v + ϕ4 4.58 = MW W µw µ + 1 M ZZ µ Z µ + gm W ϕ + g 4 ϕ W µw µ 1 + Z cos µ Z µ θ W + µ ϕ M Hϕ 1 M H λϕ 3 λ 4 ϕ4 +const. 4.59. g, g, λ v/ W M W, Z M Z, M H. 4.33 W µ, Z µ, A µ, L gauge = 1 4 F A µνf Aµν 1 4 F Z µνf Zµν 1 D µw ν D ν W µ D µ W ν D ν W µ., +i ef A µν + g cos θ W F Z µν + g W µ W ν W µ W µ W µ W µ 4.60 F X µν µ X ν ν X µ 4.61 e = g sin θ W = gg g + g 4.6 ga 3 µ = g sin θ W A µ + g cos θ W Z µ 4.63 = ea µ + g cos θ W 4.64 D µ W ν = µ + iga 3 µ Wν 4.65 = µ + iea µ + ig cos θ W Z µ W ν 4.66 0

. 4.66 W µ Q = +1. 4.5 SU L T = 1/, Y = 1, SU L 1 T = 0, Y =. 1 3 T = 1 νe νµ ντ Y = 1 L e L µ L τ e µ τ L L L T = 0 Y = R e e R R µ µ R R τ τ R 4.31 Q = T 3 + Y/, Q, ν el Q = + 1 + 1 1 = 0 4.67 e L Q = 1 + 1 1 = 1 4.68 e R Q = 0 + 1 = 1 4.69. ν er, ν µr, ν τ R,., Q = 0, SU L 1 T = 0, Y = 0,,.. L int. lepton = j=e,µ,τ + j=e,µ,τ = g L lepton = L int. lepton + L mass lepton 4.70 L j iγ µ µ i g B µ + ig τ A µ L j R j iγ µ µ ig B µ R j 4.71 W µ J µ + W µ J µ eaµ J µ em g cos θ W Z µ J µ Z4.7 1

.., J µ em = J µ = j=e,µ,τ j=e,µ,τ jγ µ j 4.73 jγ µ 1 γ 5 ν j 4.74 J µ Z = j µ 3 sin θ W J µ em 4.75. j a µ 4.8.,. 4.5.1. W g µν p M W 4.76. p W M W g 8 1 M W = G 4.77. G = g 8M W = g 8 1 gv = 1 v 4.78, 4.,. v 46 GeV 4.79 1 g e 1 M W = = 8 G 8G sin = 37.3 GeV 4.80 θ W sin θ W M Z = M W cos θ W = 37.3 GeV = 74.6 GeV 4.81 cos θ W sin θ W sin θ W

4.5.. Z θ W. 197 1973, sin θ W 0.3., M W 78 GeV, M Z 87 GeV. 1983 W Z. 017, M W = 80.385 ± 0.015 GeV 4.8 M Z = 91.1876 ± 0.001 GeV 4.83,,. 4.6, L mass lepton. mψψ., P R = 1 + γ5 4.84 P L = 1 γ5 4.85 P R = P R 4.86 P R = P R 4.87 ψ = ψ γ 0 4.88 γ 5 γ 0 = γ 0 γ 5 4.89 ψψ = ψ P R + P L ψ 4.90 = ψ P R P R + P L P L ψ 4.91 = ψp R PR ψ + ψp L PL ψ 4.9 = P L ψ P R ψ + P R ψ P L ψ 4.93 = ψ L ψ R + ψ R ψ L 4.94 3

. SU L,, 1, ψψ, SU L. ν e e. Φ, f e Le Φ R e + h.c. 4.95, L e = ν el e L 4.96 Φ = ϕ1 ϕ + = ϕ ϕ 0 4.97 R e = e R 4.98, L e Φ 1, 1, SU L., f e 1/ 0, h.c.. Y, L e L e 1, Φ +1, R e 1 + +1 + = 0 4.99, U1 Y. 4.95, f e νel e L 0 v e R + h.c. 4.100 = f e v e L e R + h.c. 4.101 = f e v e L e R + e R e L 4.10 = m e ee 4.103., m e = f ev 4.104, f e v/ m e.. f e = me v = m e g 4.105 MW 4

. 3 L mass lepton L mass lepton = j=e,µ,τ f j [ Li Φ R j + R j ϕ L j ] 4.106.., 0. 4.106 f j. G ij, L mass,gen. lepton = i,j=e,µ,τ [ Gij Li Φ R j + G ijr j ϕ L j ] 4.107., U L U R. G = U LF U R 4.108 F, F ij i j, F ij = 0. R i = j L i = j U Rij R j 4.109 U Lij L j 4.110, R i R i, L i L i, F jj = f j, L mass lepton.,.,,, CKM. 5

4.7 CKM, 3. Q 1 3 u A + 3 u c t A = 1,, 3 d A 1 3 d s b SU L, SU L 1. 1 3 u c t T = 1 Y = + 1 q 3 L1 = q L = q L3 = d s b T = 0 Y = + 4 3 u R c R t R Y = 3 d R s R b R L L L Q = T 3 + Y/ u L Q = + 1 + 1 + 1 = + 3 3 d L Q = 1 + 1 + 1 = 1 3 3 u R Q = 0 + 1 + 4 = + 3 3 d R Q = 0 + 1 = 1 3 3 4.111 4.11 4.113 4.114. L quark, L int. quark L int. quark = A L quark = L int. quark + L mass quark 4.115 { q W LA iγ µ µ + ig 16 B µ + ig τ A µ q W LA 6

+u W RA iγ µ µ + ig 3 B µ +d W RA iγ µ µ ig 1 3 B µ u W RA } d W RA 4.116. W. L mass quark L mass quark = d f ABq W LA Φd W RB + f u A,B ABq W LA Φu W RB + h.c. 4.117., Φ iτ Φ 4.118 0 i τ = 4.119 i 0 0 1 0 Φ 0 = 0 v = 4.10 1 0 v 0, u A. f X AB,., L mass quark = A,B 1 f ABvd d W LA d W RB + 1 f ABvu u W LA u W RB + h.c. 4.11. f X AB S X T X X = d, u,, m X A. C,D,. S 1 X f X AC CD v T X DB = m X A δ AB 4.1 S XF T X = M 4.13 7

ψ W ψ M S X T X. d W LA = B u W LA = B d W RA = B u W RA = B S d AB d M LB 4.14 S u AB u M LB 4.15 T d AB d M RB 4.16 T u AB u M RB 4.17. J µ em J em µ = + 3 A = + 3 A u W A γ µ u W A 1 3 u M A γ µ u M A 1 3 A A d W A γ µ d W A 4.18 d M A γ µ d M A 4.19., W, M. J µ Z, J µ Z = j µ 3 sin θ W J µ em 4.130 j µ 3 = A = 1 4 A = 1 { 4 q W LA γ µ τ 3 A. J µ qw LA 4.131 { u W A γ µ 1 γ 5 u W A d W A γ µ 1 γ 5 d W A u M A γ µ 1 γ 5 u M A d M A } 4.13 } γ µ 1 γ 5 d M A 4.133 J µ = A u W A γ µ 1 γ 5 d W A 4.134 = u W LA γ µ d W LA 4.135 A = u M LA γ µ S u S d AB dm LB 4.136 A,B 8

., V CKM S us d 4.137 CKM... CKM V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb 4.138. 3, 1. CKM,,., i=u,c,t m=d,s,b V CKMV CKM = V CKM V CKM = I 4.139 V imv in = δ mn m, n = d, s, b 4.140 V im V jm = δ ij i, j = u, c, t 4.141., 4.141 m = b, n = d, V ubv ud + V cbv cd + V tbv td = 0 4.14, VubV ud, VcbV cd, VtbV td 3. 3 3.. 4.8 CP, CP. CKM. P, x µ ψx µ. x µ = t, r x µ = t, r 4.143 ψx µ γ 0 ψx µ 4.144 9

C, ψ. ψ ψ c 4.145 = Cψ T 4.146 = iγ 0 γ ψ T 4.147, T. P C CP. CP, CP,. 4.9 3, 3. C CP, CP. 4.10 K CP K d s. K 0 ds 4.148 K 0 ds 4.149 K 0 K 0, 1. P K 0 = K 0 4.150 P K 0 = K 0 4.151 30

K 0 K 0 1. CP,. K 0 K 0. C K 0 = K 0 4.15 C K 0 = K 0 4.153 CP K 0 = K 0 4.154 CP K 0 = K 0 4.155 K 1 = 1 K 0 + K 0 4.156 K = 1 K 0 K 0 4.157 K 1 K CP +1 1. K 0 K 0 W. K.. g 4 i,j=u,c,t V is VidV js Vjd K 0 π 0 π 0 4.158 K 0 π + π 4.159 K 0 π 0 π 0 4.160 K 0 π + π 4.161., π π + ud 4.16 π ud 4.163 1 π 0 uu dd 4.164. 31

K π, 0., π l = 0. P π i, π j = 1 1 l=0 π j, π i = π j, π i 4.165, i, j 0, 0, +,,, +.,, CP +1. C π i, π j = π j, π i 4.166 CP π i, π j = π i, π j 4.167 3, K 0 π 0 π 0 π 0 4.168 K 0 π 0 π 0 π 0 4.169 3., 3 π l 1 l. P π 0, π 0, π 0 = 1 3 1 l 1+l π 0, π 0, π 0 = π 0, π 0, π 0 4.170 +1., CP 1., C π 0, π 0, π 0 = π 0, π 0, π 0 4.171 CP π 0, π 0, π 0 = π 0, π 0, π 0 4.17 K 0 π + π π 0 4.173 K 0 π + π π 0 4.174,, CP. K 1, K 3,,. 3

K 1 π 0 π 0, π + π, π + π π 0 K π 0 π 0 π 0, π + π π 0, cτ =.7 cm KS 0, cτ = 15 m KL 0. KS 0 CP +1 K 1, KL 0 CP 1 K., KL 0 CP +1 π+ π. CP π 0 π 0 π 0 19% π + π π 0 13% π + π + 0.% CP K 0 L CP. 1 KL 0 CP CP K 0 S = K 0 L = 1 1 + ε K 1 + ε K 4.175 1 1 + ε ε K 1 + K 4.176, ε = 10 3. CP CP CKM.,,.. 33

5 5.1 SU3 QCD. SU3 c, c color.. g s. T a 3 1 = 8, λ a, T a = λ a., 0 1 0 0 i 0 1 0 0 λ 1 = 1 0 0 λ = i 0 0 λ 3 = 0 1 0 0 0 0 0 0 0 0 0 0 λ 4 = λ 6 = 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 λ 5 = λ 7 = 0 0 i 0 0 0 i 0 0 0 0 0 0 0 i 0 i 0. T a. f abc, λ 8 = 1 3 1 0 0 0 1 0 0 0 5.1 5. trt a = 0 5.3 trt a T b = 1 δ ab 5.4 [T a, T b ] = if abc T c 5.5 f 13 = 1 5.6 34

f 147 = f 165 = f 46 = f 57 = f 345 = f 376 = 1 5.7 f 458 = f 678 = 3 5.8 SU3 c, q 3 3, triplet, q 3, g 8. 1.,, W, Z, 1.. qq 3 3 = 1 8, 3 qqq 3 3 3 = 3 6 3 = 1 8 8 10. 1. 5., q f G a µ,. L QCD = q f iγ µ µ + ig s G a λ a µ m f q f f a 1 G a 4 µνg aµν + g sθ G a a 3π G µν aµν 5.9 a, G a µν µ G a ν ν G a µ g s f abc G b µg c ν 5.10 G aµν 1 εµνλρ G a λρ 5.11, ε µνλρ 4..., 5.9. CP, θ θ < 10 9. 1, θ. Peccei-Quinn, θ = 0, NG 35 b,c

... 5.3 QED V r = e 1 4π r = α r 5.1. α. V Q = V re iq r d r 5.13. Q. = e Q 5.14 V Q = e 1 Q 1 e 1π log Q 5.15 4m e. Q, αq = e Q 4π = = e 0 4π α 0 1 1 e 0 1π log Q 4m e 5.16 1 α 0 log 5.17 Q 3π 4m e. µ, αq = αµ 1 αµ log 5.18 Q 3π µ. Q α. 36

QCD, α s α s Q = g sq 4π = α s µ 1 + αsµ 33 n 1π f log 5.19 Q µ., n f, n f = 6,. α, Q α s.. Q r. V r = α s /r, r 1, log Q, r,. 37