Week 4 (due Feb. 5)
In the last three problems it is better to use the FeynCalc.m package for
Mathematica than to do gamma-matrix traces by hand. See http:/www.feyncalc.org/
for detailed info on this package.
1. Problem 40.1.
2. Problem 45.2
3. Problem 48
Homework 1 Solutions
Ph 205b
1. The Lorentz group in three spacetime dimensions is three dimensional because there
is one way to rotate (in the x-y plane) and two ways to boost (in either the x or y
directions). Alternatively, there are three generators o
Week 9 (due March 12)
1. (20 its). Consider Dirac fermions coupled to a background scalar
eld (x) via the interaction Lint = g . Compute the low-energy eective
Hamiltonian for the nonrelativistic Fermi eld describing the electron to order
p2 /m2 .
2. (20
Week 7 (due Feb. 26)
1. Using the Poisson brackets for electric and magnetic elds in Maxwell
theory (derived in class) and the Hamiltonian
H=
1
d3 x (E 2 + B 2 ),
2
derive the Hamiltonian equations of motion and show that they are equivalent
to six out of
Week 5 (due Feb. 12)
1. Problem 48.5 (ab) (20pts).
2. Problem 52.3 (abcdefg) (50pts).
3. Consider a theory of Dirac fermions with mass m interacting via a
quartic interaction
Lint = g .
It describes spin-1/2 particles and anti-particles. In the nonrelativ
Week 1 (due Jan. 15)
1. (20pts) Consider Lorenz group in three-dimensional space-time (i.e.
one timelike direction, two spacelike directions). Show that the group is
three-dimensional. Construct a 2-1 homomorphism from SL(2, R) (the group
of real 2 2 matr