LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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An elementary example illustrates basic problems with gauge invariance<br />
A CHARGED PARTICLE IN A CONSTANT ELECTRIC FIELD<br />
ONE-DIMENSIONAL TREATMENT<br />
Classical electrostatics is a complete field in itself. It can be done<br />
exclusively with scalar potentials.<br />
Elementary example: a particle of mass m and charge q in a constant<br />
electric field E 0 . This can be done in one dimension x.<br />
Hamiltonian: H = p 2 /2m – qE 0 x<br />
Hamilton’s equations:<br />
x<br />
<br />
H<br />
p<br />
<br />
p<br />
m<br />
;<br />
p<br />
<br />
H<br />
x<br />
<br />
qE 0<br />
10
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