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Quantum Field Theory. Note
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Spontaneous symmetry breaking. Higgs mechanism.
(Moulders,chapter 12)
Goldstone theorem.
If a theory has a symmetry, such as SO(2) symmetry,
L = ½ (∂
μ
σ∂
μ
σ + ∂
μ
π∂
μ
π) - V(π
2
+σ
2
)
V(S) = ½ m
2
S + λ S
2
which is not the symmetry of the ground state (vacuum)
m
2
< 0 , λ > 0 ⇒ S
0
= -
m
2
/
4λ
≠ 0
then the theory will have a massive particle and a massless particle.
Higgs mechanism.
If the symmetry breaking happens in a gauge theory
L = ½ D
μ
φ D
μ
φ - V(φ
2
) -
1
/
4
G
μν
G
μν
than a massive scalar particle appears, called Higgs boson, and some gauge bosons become massive.
Exercises
Take the pensumlist and mark with one, two, or three stars the items according to how well in your opinion they fit within the course.
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D.V.Fedorov
(
fedorov@ifa.au.dk
)