Nonlocality of gauge-charged particle?
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1Another problem related to the nonlocal behaviour of the Coulomb gauge potential .... retarded magnetic field of the charged particle .... . .. .
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A charged local operator transforms under gauge symmetry as
O(x)→e−iqα(x)O(x).O(x)→e−iqα(x)O(x).
where qq is the charge of the state. We now construct the operator
O~(x)=WP,q(∞,x)O(x)O~(x)=WP,q(∞,x)O(x)
This transforms as
O~(x)→e−iqα(∞)O~(x).O~(x)→e−iqα(∞)O~(x).
Then, O~(x)O~(x) is invariant under local gauge transformations but not invariant under global symmetry transformations.
O(x)→e−iqα(x)O(x).O(x)→e−iqα(x)O(x).
where qq is the charge of the state. We now construct the operator
O~(x)=WP,q(∞,x)O(x)O~(x)=WP,q(∞,x)O(x)
This transforms as
O~(x)→e−iqα(∞)O~(x).O~(x)→e−iqα(∞)O~(x).
Then, O~(x)O~(x) is invariant under local gauge transformations but not invariant under global symmetry transformations.
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