Suppose you have two charged particles that interact by e.m. potential ##V(\vec{r_1},\vec{r_2})##, the total charge is conserved. Since there's a conserved quantity, it must exist a transformation for which the hamiltonian is invariant (Noether theorem). Let's be the operator ##U## ##(U^{\dagger}=U^{-1})## the generator of the aforementioned trasformation, you have that:(adsbygoogle = window.adsbygoogle || []).push({});

##H'=U^{\dagger}HU##

and

##H'=H##

so that

##[H,U]=0##

Now the questions are:

What is ##U##?

Is ##U## a continuous or discrete transformation?

Is ##U## an observable (##U=U^{\dagger}##)?

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# About charge conservation

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