LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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<strong>GAUGE</strong> TRANSFORMATION<br />
1 <br />
xE0<br />
' 0<br />
c t<br />
<br />
A 0 A'<br />
A cE0t<br />
x<br />
2<br />
p<br />
1<br />
H qxE0 H ' p ' qE0t<br />
2m<br />
2m<br />
Transformed Hamilton’s equations are:<br />
x<br />
H'<br />
p ' qE t H'<br />
, ' 0<br />
p ' m x<br />
0<br />
p <br />
mx<br />
<br />
qE<br />
These equations can be combined to give: 0<br />
THE EQUATION <strong>OF</strong> MOTION IS AS BEFORE.<br />
<strong>GAUGE</strong> <strong>INVARIANCE</strong> IS SATISFIED!<br />
<br />
2<br />
12
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