Quantum Field Theory II
Problem Set 5
Prof. C. Armendariz-Picon
Due Oct. 9, 2008
Exercise 18: Eective action in the presence of a background eld
Consider the generator of connected correlation functions in the presence of a (not necessarily
constant) back
Quantum Field Theory II
Problem Set 1
Prof. C. Armendariz-Picon
Due Sept. 11, 2006
Exercise 1: Statistics and Gaussian integrals
In this problem set we explore dierent properties of Gaussian integrals. They will be the
foundation of our evaluation of path
Quantum Field Theory II
Problem Set 3
Prof. C. Armendariz-Picon
Due Sept. 25, 2006
Exercise 10: Radiative corrections in 4
Write down (but do not try to calculate explicitly) all the radiative corrections to the propagator to 2nd order in in the theory
1
Quantum Field Theory II
Problem Set 12
Prof. C. Armendariz-Picon
Due Dec. 4, 2008
Exercise 33: Weyl Spinor Lagrangian
Verify that the Lagrangian
1
1
L = i m m
2
2
(1)
leads to a real action.
Exercise 34: Weyl spinors
Verify that the Dirac Lagrangian
L =
Quantum Field Theory II
Problem Set 2
Prof. C. Armendariz-Picon
Due Sept. 18, 2006
Exercise 4: Projecting onto the out-vacuum
Show that
out (t t
out )
f
lim
tf (1i )
f , tf | = f |0out eiE0
and
out (t t
out )
f
e E0
0out |U (tout , t0 )
0out |U (tout , t0
Quantum Field Theory II
Problem Set 4
Prof. C. Armendariz-Picon
Due Oct. 2, 2006
Exercise 15: The Coleman-Weinberg potential
Use
d d p E f (p 2 ) =
E
2 d/2
(d/2)
dpE pd1 f (p2 )
E
E
(1)
to show that the cut-o one-loop contribution to the eective potential
Quantum Field Theory II
Problem Set 6
Prof. C. Armendariz-Picon
Due Oct. 16, 2008
Exercise 21: Vector eld propagator
Calculate the momentum-space propagator of a vector eld
1
1
L = F F m2 A A ,
4
2
(1)
using the path integral approach.
Exercise 22: Vector
Quantum Field Theory II
Problem Set 7
Prof. C. Armendariz-Picon
Due Oct. 23, 2008
Exercise 25: Kllen-Lehman representation
a
Prove the equation
1
(2 )3
d3 p
[(x0 y 0 )eip(xy) + (y 0 x0 )eip(xy) ] =
0
2p
eip(xy)
d4 p
.
(2 )4 p2 + 2 i
(1)
On the right-hand-
Quantum Field Theory II
Problem Set 12
Prof. C. Armendariz-Picon
Due Dec. 11, 2008
Exercise 39: Feynman rules in non-Abelian gauge theories
The gauge-xed Yang-Mills Lagrangian is
1
1
Lmod = F F A A + ,
4
2
(1)
F = A A + g C A A .
(2)
where
Find the gauge
Quantum Field Theory II
Problem Set 10
Prof. C. Armendariz-Picon
Due Nov. 20, 2008
Exercise 32: Low energy calculations
In exercise 30 you have calculated the leading contribution to elastic scattering of Goldstone
bosons, which is of order (E/M )4 (E sta
Quantum Field Theory II
Problem Set 9
Prof. C. Armendariz-Picon
Due Nov. 13, 2008
Exercise 29: Universality of function coecients
Show that the rst two coecients of the function are universal, that is, they do not depend
on the precise nature of the renor