Physics 443 Homework 5 Solutions
Problem 1 (P&S Problem 4.4)
a)
T
p |S |p =
lim
T (1i )
p | exp i
dt
d3 xe A
|p .
(1)
T
Ignoring the trivial identity contribution and working to the lowest order in e we nd
d4 x p | |p A .
p | iT |p = ( ie)
(2)
Since both
Physics 443 Homework 4 Solutions
Problem 1
a)
For p = 0 (which gives a standard timelike vector) L(p) = . For = L(q ) we have
~
X
X
[us0 (~)]i D [W (L(q ), p)]s0 s =
q
1/2 [L(q )]ij [us (0)]j .
s0
(1)
j
Since L(q )p = q and W (, p) = L
1
(p)L(p), the corr
Physics 443 Homework 3 Solutions
Problem 1 (P&S Problem 3.4)
a)
Under a Lorentz transformation the eld transforms as
(x) (x ) = L (x),
(1)
where x = x. We will show that (x) = L (1 x) satises the eld equations if (x) satises them.
One can read from the re
Physics 443 Homework 1 Solutions
Problem 1 (P&S Problem 2.1)
a)
Varying the action with respect to A we nd that
1
4
1
=
2
1
=
2
S =
=
d4 x (F F )
(1)
d4 xF F
(2)
d4 x ( A A ) F
(3)
d4 x A F .
(4)
So the equations of motion are given by F = 0.
Above, we