LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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These equations can be combined to give:<br />
x<br />
qE ,<br />
m<br />
0<br />
This is Newton’s equation: (mass)(acceleration) = force<br />
The solution is elementary; it is quadratic in time.<br />
Now a simple gauge transformation will be applied.<br />
What has been done above corresponds to what is often called the<br />
length gauge, because the interaction term in the Hamiltonian has the<br />
form – E 0 x . The gauge transformation to be applied eliminates the<br />
scalar potential and introduces a one-dimensional version of a vector<br />
potential. This is called the velocity gauge.<br />
The gauge transformation has the generating function<br />
= - cE 0 x t<br />
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