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[QUOTE="A. Neumaier, post: 6823803, member: 293806"] Yes, there should be no problem; I deliberately kept the setting very simple. But this does not mean that nothing needs to be discussed. We consider explicitly only the part of the lab containing the beam, assuming the beam goes through a perfect vacuum. Restricting the state to this region, it is a vacuum state before the source is switched on. Your creation operators only affect the state at other positions where there is lab matter, hence have no effect on the beam. (This holds since the Hilbert space of the quantum field theory is the completion of a tensor product of the Hilbert spaces of the regions into which one partitions space.) Thus as long as we exclude what happens at the source (and later at a magnet or a screen) we only need to work with the vacuum state and a free field Hamiltonian. We may ignore the composition of a silver atom (made from elementary particles). Moreover, since silver is heavy, we may use nonrelativistic quantum field theory, so problems with renormalization are absent. This makes the discussion feasible. Everything that happens is encoded in the Heisenberg equation for the dynamics of the observables. Since the beam is directed along the ##z## axis, the behavior of the source (and hence the detailed properties of the beam) enters solely through the time-dependent ingoing boundary conditions at ##z=0##. [/QUOTE]
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