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I am confused with the Bohm-Aharonov effect: though quantum mechanics is said to be gauge invariant, the presence of a solenoid imposes a gauge. I used to think that a phase shift did not change anything in the physical interpretation, though here the phase shift changes the double slit experiment.

I realise after reading books and articles that I must be wrong somewhere but am unable to find out.

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The change of the overall phase of the wave function $$ |\psi \rangle \to e^{i\phi} |\psi\rangle $$ has no physical implications. However, the change of the relative phase of two terms in the wave function always has physical consequences. In particular, in the Bohm-Aharonov effect, the particle may avoid the solenoid on the left side or the right side – the analogy of two slits in a double-slit experiment. The relative phase $\phi_R-\phi_L$ between the two components of the wave function influence the interference pattern.

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And of course the phase difference is gauge invariant :-). –  FraSchelle Apr 25 '13 at 22:42
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