QFT 3 : Problem Set 2
1.) Peskin & Schroeder 16.1 Arnowitt-Fickler gauge
In this problem we are supposed to look at the Faddeev-Popov (FP) quantization of Yang-Mills (YM)
theory in the Arnowitt-Fickler gauge:
LYM
A
3a
1a
= (F )2 + (iD m)
4
=0
(1)
(2)
Let
QFT 3 : Problem Set 5
1.) Peskin & Schroeder 19.2 Weak decay of the pion.
(a.)
In this section we are working with the Lagrangian:
L =
4 GF
(lL L ) (uL dL ) + h.c.
2
(1)
We need to express the hadronic part of the operator for semileptonic weak interacti
QFT 3 : Problem Set 6
1.) Peskin & Schroeder 19.3 Computation of Anomaly coecients
(a.)
A product r1 r2 of SU (n) representations may be decomposed into its irreducible representation as
follows:
r1 r2 =
ri
(1)
i
The representation matrices in the represe
QFT 3 : Problem Set 4
1.) Peskin & Schroeder 18.1 Matrix element for proton decay
(a.)
Let us view this problem in light of section 18.1 in the text. The operator we are concerned with is the
given eective Lagrangian:
L
=
2
m2
X
abc
eR uRa uLb dLc
(1)
Th
PHYS445 Spring 2013: Problem Set 3 Solutions
1.) Peskin & Schroeder 17.1 Two-loop renormalization group relations
(a.)
We have been given the QCD -function:
(g ) =
b1 5
b2 7
b0 3
g
g
g + .
(4 )2
(4 )4
(4 )6
(1)
The renormalization group equation for g g
QFT 3 : Problem Set 1
1.) Peskin & Schroeder 15.1
(a.)
The basis for the fundamental representation of SU(N) is formed by N N traceless Hermitian matrices.
The number of such matrices is = N 2 1.
For SU(3) this number evaluates to = 32 1 = 8.
(b.)
For thi