LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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By hypothesis, the laser pulse is finite, so<br />
H<br />
t<br />
H 0<br />
lim<br />
0 <br />
t<br />
We can organize the two complete sets of states and states so that they<br />
correspond at t - :<br />
lim<br />
t<br />
<br />
t<br />
t<br />
0<br />
n<br />
After the laser interaction has occurred, the only way for the laboratory instruments to<br />
discover what has happened is to form overlaps of all possible final f states with the<br />
state that began as a particular i state. This is the S matrix:<br />
S<br />
fi<br />
<br />
lim<br />
t<br />
<br />
<br />
n<br />
f<br />
, <br />
Subtract the amplitude that no transition has occurred:<br />
i<br />
<br />
M<br />
fi<br />
<br />
S<br />
1<br />
lim <br />
, <br />
lim <br />
, <br />
fi<br />
t<br />
f<br />
i<br />
t<br />
f<br />
i<br />
45
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