ФИАН / Nefedyev_Ktp
.pdf[Aµ(x)Aν (y)]
{ ¯ }
ψα(x)ψβ (y)
C
P
T
CP T
T S
S
1 + 2 → 3 + 4
1 + 2 → 3 + 4
SU(N)
π0 → γγ
e+e−
ep
e+e− pp¯
λϕ4
λϕ4
D
D
α = 1 e2 ≈ 1/137.03599911,
4π ~c
α
ψ(x, t)
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∂ |
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Lψ = 0, L = i~ |
∂t |
− H, |
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L |
E M M
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gµν = (1, −1, −1, −1), δµν = (1, 1, 1, 1).
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AµBµ = δµν AµBν = gµν AµBν = A0B0 − AB.
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∂/∂t = ∂/∂x0 ≡ ∂0 |
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∂µ = |
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∂ |
= (∂0, ), ∂µ = |
∂ |
= (∂0, − ) |
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∂xµ |
∂xµ |
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∂µjµ(x) = |
∂j0 |
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∂j1 |
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∂j2 |
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∂j3 |
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∂j0 |
+ j = 0. |
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∂t |
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∂x1 |
∂x2 |
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∂x3 |
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∂t |
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∂µxν = |
∂xν |
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= δµν |
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∂xµ |
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∂µxµ = |
∂x0 |
+ (x) = δµµ = 4. |
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∂x0 |
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AµBµ ≡ A0B0 − AB.
jµ = (j0, j), ∂µ = (∂0, −),
∂µjµ = ∂0j0 − (− )j = ∂j∂t0 + j.
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1 e2 |
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α = |
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≈ |
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4π |
~c |
137 |
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√ α = e2/(~c) 4π
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V = LxLyLz |
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c ~ |
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~ = c = 1 |
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[m] = [E] = [p] = m, [t] = [x] = |
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~ ≈ 6.582 · 10−22 |
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, c ≈ 3 · 108 |
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· −1 |
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10−15 |
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~c ≈ 197.33 |
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5 |
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~ = c = 1
1 · 1 ≈ 5.
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λC = |
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= 1 . |
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0.2 |
0.2(1 |
· 1 ) |
0.2 · 5 |
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103 |
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E = |
mv2 = |
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· 10−6 |
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≈ 10−6 |
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= 6.5 · 1012 = 6.5 , |
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1.6 |
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10−19 |
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Z t2
S = Ldt,
t1
δS = 0
L(t, x, x˙ , x¨, . . .) = L(x˙ , x¨, . . .).
L |
x˙ ≡ v |
L = L(v2)
V
L |
L v2 |
m/2
L = 12mv2,
m
S = R L d4x
m4
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H |
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h1, h2 H h3 = h1 · h2 H |
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h1 · (h2 · h3) = (h1 · h2) · h3 |
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e H e · h = h |
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h−1 H h−1 · h = e |
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h1 · h2 6= h2 · h1 |
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e · h = h · e |
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h · h−1 = e |
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h−1 |
h (h−1)−1 = h |
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xµ → x′µ = Λνµxν ,
x2 = xµxµ = gµν xµxν = xT gx = x20 − x21 − x22 − x23,
O(1, 3) O
gµν = |
(1, −1, −1, −1). |
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x2 = xT gx |
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x2 = x′2 = x′T gx′ = (Λx)T g(Λx) = xT ΛT gΛ x |
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Λ = ±1 |
Λ = −1 |
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x → −x |
x0 → −x0 |
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(x0) |
0 |
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Λ = +1 |
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(Λ0) = +1 |
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SO+(1, 3) SO↑(1, 3)
Λ SO+(1, 3)
Λ |
U(Λ) |
U(Λ1Λ2) = U(Λ1)U(Λ2)
U(Λ) = exp |
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2ωµν Mµν |
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i |
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ωµν
Mµν
[Mµν Mρσ] = i (gµρMνσ − gµσMνρ − gνρMµσ + gνσMµρ) .
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Mµν |
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Ji i = 1, 2, 3 |
Ki |
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i = 1, 2, 3 |
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Ji = |
1 |
εijkMjk, |
Ki = Mi0 = −M0i, |
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[JiJj ] = iεijkJk, |
[JiKj ] = iεijkKk, |
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[KiKj ] = −iεijkJk. |
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M = |
1 |
(J − iK), |
N = |
1 |
(J |
+ iK) |
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[MiMj ] = iεijkMk, [NiNj ] = iεijkNk, |
[MiNj] = 0, |
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P : x → −x
P = −1
P
T : x0 → −x0
P T
P
P