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On the one hand, we know that the overall phase of the wave function (of the whole system) is not a measurable quantity, but more an artifact of mathematical description — the physical states are rays in the Hilbert space. The description in terms of density matrix and quantum channels lacks this redundancy (at least, explicitly).

On the other hand, in certain cases it feels like the phase is more physical than it could first seem. But this, of course, is another consequence of axioms of quantum mechanics, and we should be able to describe such situations within any of equivalent formalisms.

How would one, for example, study the Aharonov-Bohm effect using the formalism of density matrix and quantum channels?

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  • $\begingroup$ Great question, but seemingly no one has any idea about this. See my similar question $\endgroup$
    – mma
    Commented Jan 20 at 11:41
  • $\begingroup$ I don't think you want to study a relativistic effect without using the framework of a relativistic field theory. Non-relativistic theory can't even predict the periodic table correctly, so why would you trust it with an explicit interaction with a free electromagnetic field? $\endgroup$
    – FlatterMann
    Commented Jan 20 at 13:34
  • $\begingroup$ @FlatterMann why are we discussing relativity here? AB effect has a pretty good non-relativistic treatment in many textbooks... $\endgroup$
    – Mauricio
    Commented Jan 20 at 13:37
  • $\begingroup$ @Mariciao So does entanglement... it just happens to be the wrong way of going at it and that's why there are so many misunderstandings about quantum mechanics out there. Many people are still trying to do things in a Galilean framework that are not caused by Galilean physics. It only gets you so far. My suggestion would be to look at it through the lens of quantum field theory. You can ignore that suggestion at your own peril. $\endgroup$
    – FlatterMann
    Commented Jan 20 at 13:42
  • $\begingroup$ @FlatterMann do you know of any basic relativistic formulation of AB effect? $\endgroup$
    – Mauricio
    Commented Jan 20 at 14:12

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