PHY431 Homework Set 9
Reading:
Lecture Notes
Homework:
See below:
Due date:
Wednesday May 3
Hints and Solutions
Problem IX.1
Show that the SU(2) group of continuous operators exp{
i
½
σ
·
α
(
x
)}:
is unitary
.
has determinant 1
b.
Hints:
see the lecture notes
Solution:
no solution yet
Problem IX.2
Show that the Pauli matrices have the group structure defined by [
σ
i
,
σ
j
] = 2
i
ε
ijk
σ
k
.
Hints:
the tensor
ε
ijk
is the fully antisymmetric tensor under any permutation of the
indices
ijk
.
Solution:
no solution yet
Problem IX.3
Draw the Feynman diagram of
Λ→
n
+
π
0
. Show all quark lines, and indicate how
it differs from the figure next to equation (13.18) in the notes.
.
Using the Cabibbo mixing matrix, estimate the ratio of the decay amplitudes (the
Feynman factors) of the processes
Λ→
p
+
e

+
f8e5ν
e
and
n
→
p
+
e

+
f8e5ν
e
b.
Hints:
The ratio will be a ratio of Cabibbo mixing factors: express the quark states in their
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 Spring '01
 Rijssenbeek
 Physics, Work, Quantum Field Theory, Quark, Feynman, fully antisymmetric tensor

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