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I'm trying to make an argument that classically, the EM field is considered a more 'real' physical quantity than the potentials, and am tempted to say that the fact that the field carries energy & momentum is evidence of this. Now I am wondering this: Is it possible to determine the energy or momentum of the electromagnetic field 'object' from the magnetic & vector potential in a way that isn't just directly equivalent to calculating the field first?

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You can find the Hamiltonian of the potentials if you know the Lagrangian, or you can calculate the energy in reference to the work done on charges in an electric field, which the electric potential sort of comes about secondarily, because it is related to the work. The calculation is done here. As for the equivalence between the two, are you familiar with the Aharonov Bohm effect?

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  • $\begingroup$ Yeah, the AB effect is the specific context I'm considering this in. That wiki page only gives the energy of a test charge in a potential, it doesn't give any direct relation between the potential and the properties of the 'electromagnetic object'. You can't, say, consider a charge distribution of 0 inertial mass and calculate the gravitational effect of it through mass-energy equivalence or anything. $\endgroup$ – llama Dec 2 '14 at 22:10

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