Physics 619
HOMEWORK # 1
DUE SEPTEMBER 24, 2012
Problem I (Peskin and Schroeder, Problem 2.1) (10 pt)
Classical electromagnetism (with no sources) follows from the action
S=
d4 x
1
4
F F ,
where
F = A A .
(a) Derive Maxwells equations as the Euler-Lagrang
Physics 619
HOMEWORK # 2
DUE OCTOBER 4, 2012
Problem I (10 pt) :
The Dirac Lagrangian in a presence of external electromagnetic eld A is given by
L = i D m
with
D = + ie A .
(a) Derive the Euler-Lagrange equation for .
(b) Show that
D D + m2 + e S F
with
HOMEWORK # 3
Physics 619
DUE NOVEMBER 1, 2012
Problem I (5 pt)
Let be a free boson eld with the propagator D (x),
(x) (x ) = D (x x ) .
Show that
ei(x) i(0) = eD(x)D(0)
Problem II (5 pt)
Show that in D dimensions
b a b = (D 2) a ,
b a1 a2 b = 4a1 a2 + (4
Physics 619
HOMEWORK # 5
DUE DECEMBER 3, 2012
Problem I (10 pt) : Peskin, Schroeder: Problem 16.1
Problem II (10 pt)
Let T i be operators which satisfy
[T i , T j ] = i f ijk T k ,
where f ijk are structure constants of a Lie algebra. Let ci and c be oper
Physics 619: Fields II
Fall 2012
PREREQUISITES
This course is a continuation of 618 (Fields I). At Spring you have used Srednickis
textbook. It was covered almost all of Part I (spin 0), and most of Part II (spin 1/2).
Specically, in Part II chapters 34-3
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