PHY 5667 : Quantum Field Theory A, Fall 2015
September 3rd , 2015
Assignment # 2
(due Thursday September 10th , 2015)
1. Let us write the infinitesimal form of a Lorentz transformation in the vector representation
as
i
= (JV ) ,
2
where
(JV ) = i (g g )

PHY 5667 : Quantum Field Theory A, Fall 2015
October 8th , 2015
Assignment # 5
(due Thursday October 22nd , 2015)
1. Consider the action of parity (P ), time-reversal (T ), and charge-conjugation operators on
spinor quantum fields as defined in Sec. 4.2.3

PHY 5667 : Quantum Field Theory A, Fall 2015
Assignment # 1, Solutions
1. The Lagrangian for a relativistic free particle is:
Lrel = mc2 1 ,
(1)
where 1 = 1 2 , = v/c, v is the particle velocity, m is the particle mass, and c is the
velocity of light. Lre

PHY 5667 : Quantum Field Theory A, Fall 2015
Assignment # 5, Solutions
Problem 2
The time-ordered product of fermion fields is defined as
T (x)(y)
= (x)(y)(x
0 y0 ) (y)(x)(y0 x0 ) .
Writing the field operators as,
Z
d3 p
1 X s s
ipx
s s
ipx
p
(x) =
a
u
(p

PHY 5667 : Quantum Field Theory A, Fall 2015
Assignment # 2, Solutions
Problem 1
The Lorentz transformation corresponding to an infinitesimal rotation by an angle about
the x axis can be written as,
= i(JV23 ) ,
(1)
where we have defined 23 = 32 = , and

PHY 5667 : Quantum Field Theory A, Fall 2015
August 27th , 2015
Assignment # 1
(due Thursday September 3rd , 2015)
1. Write down the Lagrangian of a relativistic free particle and show that, in the limit v/c 0
(where v is the magnitude of the particle vel

PHY 5667 : Quantum Field Theory A, Fall 2015
November 24th , 2015
Final Exam
(due by Friday December 11th , 2015)
1. Show explicitly that at one loop in QED:
1.a) the three-photon vertex is zero;
1.b) the four-photon vertex is UV finite, i.e. it does not

PHY 5667 : Quantum Field Theory A, Fall 2015
Assignment # 3, Solutions
Problem 1
Consider the infinitesimal Lorentz transformation of x ,
i
x0 = x (JV ) x ,
2
(1)
where (JV ) = i( ) are the Lorentz generators in the vector representation. Substituting the

PHY 5667 : Quantum Field Theory A, Fall 2015
September 10th , 2015
Assignment # 3
(due Thursday September 24th , 2015)
1. Consider a system of fields i (x) and a Lorentz transformation acting on both field and
coordinates as follows,
x0 = x ' x +
6
X
k Xk