813 (1982) ACTA PHYSICA POLONICA No 12, By L. F. Abbott. This paper seems to be freely
available on the web, so I put it up on the course web page. We will return to the rest of the paper
later when we talk about nonAbelian gauge theories. Some of this material is also treated in
sections 11.4 and 11.5 of Peskin and Schroeder (P&S from now on) though I find Abbott easier to
read, which is why I have assigned it rather than P&S. P&S are interested in this because it helps
with a systematic treatment of renormalization. Some of this is also mentioned in section IV3 of
Zee, where the issue is symmetry breaking. I suggest that you don’t read Zee’s treatment yet. We
will return to this later. When we come back to it later on, we will also go back to the original
literature and study one of the the great classic papers of the 1970’s, “Radiative Corrections as the
Origin of Spontaneous Symmetry Breaking” by Sidney Coleman and Erick Weinberg, Phys. Rev.
D 7, 1888  1910 (1973).
Do the problem below. Make sure that you follow the rules of coherence. My preliminary plan
is to have these due in class on Thursday, Feb. 11. We can discuss this further in class. Note that
you are encouraged to discuss the problems with your colleagues in the class. But you must write
up your solution entirely on your own in L
A
T
E
X.
121
.
Consider an
L
involving four complex scalar fields with
L
=
L
0
+
L
1
(121.1)
where
L
0
=
4
X
j
=1
‡
∂
μ
φ
j
∂
μ
φ
*
j

m
2
j
φ
j
φ
*
j

λ
j
4
(
φ
j
φ
*
j
)
2
·

3
X
j
=1
4
X
k
=
j
+1
λ
jk
(
φ
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 Spring '10
 GEORGI
 Physics, Quantum Field Theory, background field method