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LIMITATIONS OF GAUGE INVARIANCE

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CLASSICAL FREE ELECTRON IN A PLANE WAVE FIELD<br />

Electron follows a figure-8 trajectory resulting from the combined action<br />

of the electric and magnetic fields.<br />

α 0 = amplitude along electric field direction<br />

β 0 = amplitude along direction of propagation<br />

α<br />

0<br />

<br />

c<br />

ω<br />

2z<br />

f<br />

,<br />

β<br />

0<br />

<br />

c<br />

ω<br />

zf<br />

4<br />

,<br />

β<br />

α<br />

0<br />

0<br />

<br />

1<br />

4<br />

zf<br />

2<br />

,<br />

z<br />

f<br />

<br />

2U<br />

mc<br />

p<br />

2

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