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253a/Schwartz
Due November 30, 2010
Problem Set 12
1. * (This problem involves path integrals, so I made it a star problem. But it is a rather
easy path integral problem, so everyone should be able to do it. The real track two parts
are marked **.)
Furry’s theorem states that
a
0

T
{
A
μ
1
(
q
1
)
A
μ
n
(
q
n
)
}
0
A
= 0
if
n
is odd. It is a conse
quence of chargeconjugation invariance.
a) In scalar QED, charge conjugation swaps
φ
and
φ
⋆
. How must
A
μ
transform so
that the Lagrangian is invariant?
b) Prove Furry’s theorem in scalar QED nonperturbatively using the path integral.
c) Does Furry’s theorem hold if the photons are o±shell or just onshell?
d) **Prove Furry’s theorem in QED.
e) **In the standard model, charge conjugation is violated by the weak interactions.
Does your proof, for correlation functions of photons, still work, or do you expect
small violations of Furry’s theorem?
2. Compton scattering, qualitatively.
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 '10
 SCHWARTZ

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