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The wave behavior of particles like electrons and neutrons (whether fermions or bosons in their spin characterization) can be explained classically too. The electromagnetic interaction force that manifests itself as f=k/r^2, have an asymptotic behavior of f=k r, i.e a space spring force, when the forces involved are large and the displacement r is very ...

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1) Yes, the charge is truly and exactly conserved. What it is confusing you, I think, is that the current for a scalar field explicitly depends on 4-potential $A$, whereas that for a spin-1/2 does not. This is obviously related to the number of derivatives in the Lagrangian kinetic term and, likewise, to the number of derivatives in the current. It can help ...

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I recommend this paper: http://www.elp.uji.es/masterNNM/docencia/refs/1995%20AJP%20Cook%20chem%20potential.pdf The authors explain in a simple and clear way the physical meaning of the chemical potential in various systems, including ideal Bose gas.

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