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Physics 253a
Final Exam: Answers
The Feynman Tree Theorem.
p
i
p2 + m2 i, i.e. at ~p 2
1. In the case of the Feynman propagator, we have poles at p0 = ~
~
p
and ~p +
i
2~p .
Lets call these ~p i and ~p + i. On the other hand, for the advanced
propagator w

Lorentz Generators
We know from considering infinitesimal transformations that the Lorentz transformation
generators must be antisymmetric, and so the only choice is an overall sign. Here they are
with he signs the way I need them, for reasons given below

Homework 3 Solutions
1
Free graviton Hamiltonian
Show that the free graviton action we discussed in class (before making it gauge- and Lorentzinvariant),
S0 = d4 x hij hij ,
(1)
yields the correct free Hamiltonian operator:
d3 p
a (p)a (
p) p0 (
p) ,
H0

Chapter 4
Quantization of Fields
Take some uniform medium that vibrates and in which waves can propagate, which
could for example be a lattice of molecules. In such system, each normal mode of the
vibration can be treated as an independent harmonic oscill

Last Latexed: March 24, 2011 at 9:38
1
Physics 504, Lecture 16
March 28, 2011
c
Copyright2009
by Joel A. Shapiro
1
More on Lorentz Transformations
We saw last time that a (proper) finite Lorentz transformation A can be
thought of as being built up from an