Chapter 12
Problem Set Solutions
12.1
Problem Set 1 Solutions
1.
y
1
=
A
x
2 + y2
x
0
(a)
(12.1)
y
y
1
1
A=
x + 2
x =0
2 + y2
2
x
x +y
0
0
(12.2)
except at x = y = 0 where A is singular.
(b) For any closed path which does not wind around x = y = 0 li
8.333: Statistical Mechanics I
Fall 2007
Test 2
Review Problems
The second in-class test will take place on Wednesday 10/24/07 from
2:30 to 4:00 pm. There will be a recitation with test review on Monday 10/22/07.
The test is closed book, and composed enti
Problems
Frank Wilczek
February 21, 2003
1. Majorana Mass and See-Saw Mechanism
a. Let be a right-handed fermion eld. Using 4-component fermion notation,
and some stated convention for Dirac matrices, construct the Majorana mass
term
LMajorana =
MC
,
(1)
104
CHAPTER 12. PROBLEM SET SOLUTIONS
12.4
Problem Set 4 Solutions
1. A nice derivation on the theoretical lower bound on Higgs mass (note experimental lower bound is H 120GeV by now) can be found in G. Attarelli,
G. Isideri, Phys. Lett. B337 p141 (94) (a
1
8.324
Quantum Field Theory II
Problem Set 6 Solutions
1. (a) Under charge conjugation, as expected, the electromagnetic current changes sign, Cj C = j . QED
is C invariant, implying both that the Lagrangian is invariant under C, hence Cj A C = j A and
C
Quantum Field Theory II (8.324) Fall 2010
Assignment 6
Please remember to put your name at the top of your paper.
Readings
Peskin & Schroeder chapters 10, 12, 13.
Weinberg vol 1 chapter 12 and Vol 2 chapter 18.
Problem Set 5
1. Furrys theorem (20 point
Problems
Frank Wilczek
February 12, 2003
1. Aharonov-Bohm eect
Consider the vector potential dened by
y
+ y2
x
Ay = 2
x + y2
Az = 0
Ax =
x2
(1)
(2)
(3)
~
a. Show that the curl of A is zero, apart possibly from the z-axis where it is
ill-dened.
b. Use Stok
1
8.324
Quantum Field Theory II
Problem Set 5 Solutions
1. We will use PS conventions in this Problem Set. We consider the scattering of high energy electrons from a
target, a process which can be described to leading order in by the following generic dia
Problems
Frank Wilczek
April 9, 2003
These problems are simply directed toward calculating the QCD function at one
loop using Feynman graphs. By doing it in several di erent ways, you will check gauge
independence and universality, as well as getting prac
1
8.324
Quantum Field Theory II
Problem Set 4 Solutions
1. (a) We are going to use Peskins conventions in order not to conict with the instructions in the problem. The
interaction vertex for this theory is ig . The amplitude for the e+ e annihilation into
8.333: Statistical Mechanics I
Fall 2007
Test 2
Review Problems
The second in-class test will take place on Wednesday 10/24/07 from
2:30 to 4:00 pm. There will be a recitation with test review on Monday 10/22/07.
The test is closed book, and composed enti
78
CHAPTER 12. PROBLEM SET SOLUTIONS
12.2
1.
Problem Set 2 Solutions
I will use a basis m, which
C = i 2 = C
(12.47)
We can dene left (light) handed Majorana elds as,
= L + (L )C
= R + (R )C
(12.48)
(12.49)
= C
= C
(12.50)
(12.51)
(L )C = ( C )R
(R
Quantum Field Theory II (8.324) Fall 2010
Assignment 4
Readings
Peskin & Schroeder chapters 6 and 7
Weinberg vol 1 chapters 10 and 11.
Note
The purpose of Prob. 1 is to remind you of techniques used in tree-level calculations involving vector and spino
86
CHAPTER 12. PROBLEM SET SOLUTIONS
12.3
Problem Set 3 Solutions
Feynman rules:
i(g0
p p0 ab
)
p2 p2
,a
(12.99)
,b
p
Figure 12.1: Feynman Rules (Equation 12.99).
Fermion:
ip
/
p2
(12.100)
p
Figure 12.2: Fermion (Equation 12.100).
Ghost:
iab
p2
a
(12.101