1
Last Latexed: September 25, 2012 at 10:21
Lecture 8
Free Dirac Particles
Oct. 1, 2012
Last time we learned that we could make a Dirac eld
=
L
R
with the Dirac equation
(i m) = 0
arising from a Lagranian density
L = (i m).
We learned that transforms unde
Physics 615
Homework #2
Fall, 2012
Due: 3 PM, Sept. 21
These problems are all examples of symmetries treated by Noethers theorem.
In evaluating L it is often easier to use the expression
L = x L + i
L
L
L
+ ( i )
+ x ,
i
i
x
in the notation of Lecture 4
Physics 615
Fall, 2012
Homework #3
Due Sept. 28 at 3:00 P.M.
1)
In lecture we dened the Pauli-Lubanski vector
1
W = P L ,
2
built of the generators of the Poincar group. Show that
e
(a) [W , P ] = 0,
nd [W , L ], and then show W 2 is a Casimir operator of
Physics 615
Homework #4
Project #1
Fall, 2012
Due: Oct. 5 at 3:00
Due: Oct. 12 at 3:00
Homework #4: [5 pts] Do problem 3.2 from Peskin and Schroeder.
This is a small problem and just a partial homework for this week. The real
work is to get started on the
Physics 615
Homework #6.
Fall, 2012
Due Oct. 22 at 3:00
1) Consider adding a cubic interaction to the lagrangian density of Eq. 4.1,
so
1
1
g
L = ( )2 m2 2 3 4 .
2
2
3!
4!
Thus the interaction hamiltonian becomes
Hint =
d3 x
g3
(x) + 4 (x)
3!
4!
which me
Last Latexed: November 7, 2012 at 15:03
Physics 615
Homework #9
1
Fall, 2012
Due: Nov. 19 at 4:00
1
[10 pts] Find the spin-averaged cross section for an electron scattering
o a very heavy Dirac particle of charge e. Do not assume me 0, but
do take the lim
1
Physics 615
Wed. Dec. 12, 2012
Homework #12
1
[5 pts] Consider a theory in which the matter elds consist of a single
complex eld, (x), equivalent to two real elds, with gauge transformations
given by a single real scalar eld (x) under which (x) ei(x) (x
Last Latexed: September 5, 2012 at 11:57
Physics 615, Lectures 1-3
1
Sept. 613, 2012
Introduction
Copyright c 2005 by Joel A. Shapiro
1
Introduction
According to the catalogue, this course is Overview of Quantum Field Theory. Why Overview? When we teach C
Last Latexed: September 12, 2012 at 17:47
Lecture 4: Noethers Theorem
1
Sept. 17, 2012
Copyright c 2002, 2005, 2006 by Joel A. Shapiro
I am sure you have heard that for every continuous transformation of the
coordinates that one can make without aecting t
Last Latexed: September 19, 2012 at 10:43
1
Lecture 5:
Sept. 20, 2012
First Applications of Noethers Theorem
Copyright c 2005 by Joel A. Shapiro
Now it is time to use the very powerful though abstract formalism Noether
developed for continuous symmetries
Last Latexed: September 19, 2012 at 13:56
Lecture 6:
The Poincar Group
e
1
Sept. 24, 2012
Copyright c 2005 by Joel A. Shapiro
Last time we saw that for a scalar eld (x), for every Poincar transfore
mation : x x + c , there is a unitary operator U () which
Last Latexed: September 19, 2012 at 14:42
Lecture 7:
Dirac and Weyl Fields
1
Sept. 27, 2012
Copyright c 2005 by Joel A. Shapiro
We have seen that we expect to construct our eld theory from elds
which transform simply under Poincar transformations, with
e
Physics 615
Fall, 2012
Homework #1
Due: Sept. 14 at 3:00 P.M.
1 Consider the Lagrangian for two free real scalar elds j with equal
masses, with
2
12
1
L=
2 .
(1)
j j m2
j
2 j =1
2
j =1
Dene without an index to be the complex eld
=
1 + i2
,
2
and rewrite