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Quantum Field Theory. Note
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Feynman diagrams in coordinate space
The n-th order term in the perturbative expantion of the S-matrix with the interaction lagrangian L
int
is
S
(n)
=
(-ig)
n
/
n!
∫ d
4
x
1
...d
4
x
n
T[ L
int
(x
1
)...L
int
(x
n
)]
According to the Wick's theorem the T-product turns into a sum of normal products with all possible combinations of propagators
T[
ψ
1
ψ
1
(φ
1
+φ
1
+
)...
ψ
n
ψ
n
(φ
n
+φ
n
+
)] = ∑
all possibilities
N[...]Δ(...)
Each term in this expansion is represented by a diagram as follows:
An integration variable x
j
is represented by a point.
A propagator Δ(x
j
-x
k
) is represented by a line (solid for fermions, dashed for bosons), connecting the points x
j
and x
k
.
A field ψ(x
j
) (φ(x
j
)) is represented by a solid (dashed) line attached to the point x
j
.
Exercises
For the interaction Lagrangian L
int
=-g
ψ
ψφ draw all distinct Feynman diagrams of the fourth order.
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© 2000-2002
D.V.Fedorov
(
fedorov@ifa.au.dk
)