LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
LIMITATIONS OF GAUGE INVARIANCE
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<strong>GAUGE</strong> TRANSFORMATIONS ARE NOT UNITARY<br />
It is widely known and easily shown that a gauge transformation applied to the<br />
Schrödinger equation gives the result<br />
( H i )' U( H i<br />
) U <br />
t<br />
where U is the unitary operator that generates the gauge transformation. Although it is true that<br />
' U<br />
in order to have form invariance of the Schrödinger equation, the first equation above<br />
will not give the unitary transformation of operators<br />
1<br />
O ' UOU <br />
if U is time-dependent.<br />
The above is a rebuttal to the statement in the Preamble:<br />
• A gauge transformation is a unitary transformation.<br />
t<br />
1<br />
48
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