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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?

mma
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mavzolej
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  • Great question, but seemingly no one has any idea about this. See my similar question – mma Jan 20 '24 at 11:41
  • 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? – FlatterMann Jan 20 '24 at 13:34
  • @FlatterMann why are we discussing relativity here? AB effect has a pretty good non-relativistic treatment in many textbooks... – Mauricio Jan 20 '24 at 13:37
  • @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. – FlatterMann Jan 20 '24 at 13:42
  • @FlatterMann do you know of any basic relativistic formulation of AB effect? – Mauricio Jan 20 '24 at 14:12
  • @Mauricio I was never interested in it, so I haven't done any literature research. All I am saying is that IF I wanted to learn about it, then I would do a dive into the relativistic field theory literature because at the core of it is a relativistic phenomenon... the motion relative to an electromagnetic field. That is already a tough one in the classical treatment. – FlatterMann Jan 20 '24 at 14:19

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