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In scalar QED, applying Noether's theorem for internal global symmetries results in a Noether current that is dependent on the gauge because of the presence of the covariant derivative.

$$j_\mu=-i(\varphi^*\partial_\mu\varphi-\varphi\partial_\mu\varphi^*)-2eA_\mu\varphi^*\varphi.$$

When integrating the current to get the conserved charge, the term dependent on the gauge doesn't obviously seem to cancel out.

My question is how do you interpret this conserved charge that depends on the gauge field? For example, when you take a free complex scalar field, the conserved charge is very simply interpreted as the difference between the number of particles and anti-particles. However, I can't find a similar simple interpretation when it is coupled to a gauge field.

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