Le groupe SU(2) ⊗ U(1) et la théorie électrofaible

SU(2) ⊗U(1)
∗
•⊗
•
∗

SU(2)L⊗U(1)
SU(2)L⊗U(1)

n→p+e−+ ¯ν
&

µ= 0,1,2,3
gµν = +1 −1−1−1
dτ =pdt2−dx2
i
γµ
Taa= 1,2..., n
τ(X) = TaXa6Y=γµYµ
Aµ
Pν
qν
Fνµ
E
B
D
H
J
F
Ei
Bj
A
S
L(x)
H
H(x)
W
W(x)

ψ(x)
ψ(x)
Jµ=¯ ψ(x)γµψ(x)
L(x) = ¯ ψ(γµi∂µ−m)ψ
A=ZL(x)d4x
(i6∂−m)ψ(x) = 0
ψ(x)
•
gµν =gµν = (1,−1,−1,−1) ²0123 =−²0123 = 1
•γ5=iγ0γ1γ2γ3(γ5)2= 1
•(2s+ 1) = 2
•
•γµ
γµγν+γνγµ= 2 gµν
•
γµγν=gµν −i σµν 6A6B= (A.B)−iσµν (AµBν)
•γµ
2σµν =i[γµ, γν]
σij