Quantum Field Theory HW 1 Solution Key
HW 1 Solution Key
1. We did an example that was very similar to this in lecture, but Id like you to do this in a slightly
dierent way. Well be computing conservation of angular momentum.
(a) Write down the Lagrangian
The Standard Model HW 4 Solution Key
HW 4 Solution Key
1. Lets manipulate some of the objects in Dirac theory. Compute:
(a) cfw_ 0 , 0
Sol.
2I
Of course, more generally,
cfw_ , = 2g I
(This inclusion of the identity matrix is an exception, not a rule).
The Standard Model HW 2 Solution Key
HW 2 Solution Key
Consider a Lagrangian density of two coupled elds, a complex scalar eld, (where may be treated
independently), and a vector eld, A . In general, we can break down the eld into three parts:
L = L,f ree
PHYSICS 750: The Standard Model Final Exam Solution Key
You have 2 hours to complete this exam. Please answer all questions clearly and completely. Make sure that
you show all of your work. Only answers written in your bluebooks will be graded.
You may re
The Standard Model HW 1 Solution Key
HW 1 Solution Key
1. Please compute the following quantities in natural units (e.g. = c = 1). All answers should be in
the units of (# GeV)n , where n is some integer (depending on the units), and # is some coecent.
(a
PHYSICS 750: The Standard Model Midterm Exam Solution Key
1. [30 points] Short Answer (6 points each)
(a) In words, explain how to determine the number of mediator particles are generated by a particular
local gauge symmetry. (E.g., there are 3 weak force
The Standard Model HW 5 Solution Key
HW 5 Key
1. Imagine an interaction Lagrangian between two real-valued scalar elds:
L = 0 3
1
where 0 has a mass, M , and the 1 is massless. This interaction allows for the decay of:
0 1 + 1 + 1
As we saw in lecture, th
The Standard Model HW 6 Solution Key
HW 6 Solution Key
1. Suppose there were a free-eld Lagrangian for a real-valued scalar doublet:
1
2
=
of the form:
L=
1
1
1 1 + 2 2 V ()
2
2
where
V () = (2 + 2 C)2
1
2
where C is a positive constant.
Not to give too
PHYSICS 750: QFT I Midterm Exam Solution Key (2012)
Midterm Exam Solution Key
1. [25 points] A few quickies on special relativity. Consider a function of spacetime:
f (x ) = x2 + y 2 + z 2 t2
(a) Compute the components of f and f .
Sol.
They are:
2t
2x
Quantum Field Theory HW 4 Solution Key
HW 4 Solution Key
1. We have done several decay and scattering problems in this class with exactly 2 outgoing particles.
Those problems are in a sense too simple. For this problem, you will solve a simple decay into
PHYSICS 750: QFT Final Exam Solution Key (2012)
Final Exam Solution Key
1. [25 points] As a reminder, two of the momentum eigenstates for the Dirac equation are:
v (1) (p) =
E + m
px ipy
E p +m
pz
E p +m
0
1
v (2) (p) =
E + m
pz
E p +m
px +ipy
E p +m
1
0
PHYSICS 750: QFT I Final Exam Solution (2010)
Final Exam Solution
1. [40 points] Consider the following interaction:
e + e+ e + e+
(a) Draw all possible Feynman Diagrams with 2 vertices. For each, please indicate whether the nal
scattering amplitude shoul
PHYSICS 750: QFT I Final Exam (2010)
Final Exam
You have 2 hours to complete this exam. Please write all of your answers in a blue book. Except for the
equation sheet, this exam is entirely closer book.
Please let me know if you have any questions.
Some U
Quantum Field Theory HW 2 Solution Key
HW 2 Solution Key
1. In class, we showed that the general solution to the Klein-Gordon equation is:
(x) =
d3 p
(2 )3
1
ap ei(pxEp t) + ap ei(pxEp t)
2Ep
(a) What is the energy for this eld? For both this and for subs
Quantum Field Theory HW 3 Solution Key
HW 3 Solution Key
1. Since were doing quantum cross sections, it might help for you to compute a classical cross section.
In this problem, youre expected to use physical constants 0 , e, etc.
(a) Consider a stationar
PHYSICS 750: QFT I Midterm Exam Solution (2010)
Midterm Exam Solution
1. [30 points] Consider the (classical) complex Lagrangian density:
L = M 2
(a) Humor me. Please compute all possible Euler-Lagrange equations.
Sol.
There are, of course, two, one for
PHYSICS 750: QFT I Midterm Exam (2010)
Midterm Exam
You have 1.5 hours to complete this exam. Please write all of your answers in a blue book.
Except for the equation sheet, this exam is entirely closer book.
Please let me know if you have any questions.
Quantum Field Theory HW 5 Solution Key
HW 5 Solution Key
1. In class, I gave you the classical eld EM Lagrangian:
1
L = F F
4
where
F A A
(a) Assuming the expansion:
A (x) =
d3 p
(2 )3
1
(r )
(r )
(r) (p) ap eipx + ap eipx
2Ep
where you may assume there a