LIMITATIONS OF GAUGE INVARIANCE

We now have the form of a perfect differential:
Mfi
dt
f
, i
t
M
M
M
M
fi
fi
fi
fi
i
t
i
t
i
dt
,
,
H
H
iH
H
dt
dt
0
0
t
iH ,
, iH
H
i
,H
i
, H
H
f
f
f
0
0
dt ,H
i
H iH
I
t
f
I
i
i
An alternative form is especially useful for strong-field problems. Instead of making a
one-to-one correspondence of and states at t - , do it at t + and then
look for the probabilities that particular initial states could have led to this final result.
i
f
t
f
t
0
f
i
0
0
0
I
I
i
I
i
46