8.325 Homework 2
Iain Stewart, Feb. 23, 2007
Due: In lecture March 8.
Problem 1) MS beta-function with multiple dimensionful couplings
Consider a eld theory with a set of couplings g1 , g2 , . . ., g , . . . which well call . Your
g
goal is to derive an e
8.325 Homework 5
Iain Stewart, April 7, 2007
Due: Thur. April 19.
Problem 1) Higgs Self-Coupling
Consider the beta-function for the Higgs self-coupling
d
1
9
27 4
9
9
=
1 2 2 g 2 9 g 2 +
g + g 2 g 2 + g 4 + 4T 4 H
2
2
d
16
5
100
10
4
2
(1)
where g , g are
8.325 Homework 3
Iain Stewart, Mar. 10, 2007
Due: In lecture March 22.
Problem 1) Composite Operator Renormalization
In lecture we discussed the renormalization of parameters in a Lagrangian. Often one is inter
ested in studying a local current built from
8.325 Homework 1
Iain Stewart, February 11, 2007
Due: In lecture Feb. 22.
Problem 1) Practice with Local and Global Symmetry
Consider the theory
/
/
L = L1 + L2 = 1 iD1 1 + 2 iD2 2
(1)
where iDj = i + g A Tja . In terms of the Pauli matrices we have
a
a
T
8.325 Homework 7
Iain Stewart, May 6, 2007
Due: Thur. May 17.
Problem 1) Some algebra used to study -vacua and instantons
a) Let G = G and
K = 2 Tr G A +
2i
A A A
3
(1)
and show that K = Tr[G G ]. Feel free to use the Bianchi identity, D G = 0,
without pr
8.325 Homework 4
Iain Stewart, Mar. 23, 2007
Due: MONDAY April 9.
Problem 1) Peskin & Schroeder 20.1 (Spontaneous Breaking of SU(5)
Problem 2) Peskin & Schroeder 20.2(b) (Z-Decays)
Problem 3) Peskin & Schroeder 20.5 (A Model with Two Higgs)
Problem 4) Pes
8.325 Homework 6
Iain Stewart, April 20, 2007
Due: Thur. May 3.
Problem 1) Peskin & Schroeder, Problem 19.1, page 686-687
Problem 2) Axial-Anomaly in Dimensional Regularization
Compute the axial anomaly for QED in four-dimensions from the triangle diagram