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I was given a problem by my professor, which belongs to Migdal. The problem is as follows:

If a particle is rotated by 2$\pi$ in a magnetic field its wave-function $\psi$ transforms into $\exp(i\phi A) \psi$, where $\phi$ is given by the perimeter of the circle, while if the field were that of a strong force, $\phi$ is given by the area of the circle.

Can anybody refer me to the paper where all these are calculated? I'll appreciate your answers.

However, just explaining why $\psi$ transforms into $\exp(i\phi A) \psi$, will be a great help (suppose the case of magnetic field).

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  • $\begingroup$ Comment to the post (v6): It seems the various editors wildly disagree which tags to use! Reviewers: If you are thinking of voting-to-close, please consult the original version (v1) first. $\endgroup$
    – Qmechanic ♦
    Commented Aug 2, 2016 at 20:19
  • $\begingroup$ Cannot your professor point you in the right direction? $\endgroup$
    – sammy gerbil
    Commented Aug 2, 2016 at 23:31
  • $\begingroup$ @N.S. Googling something lame like "magnetic field migdal" brought up this page: books.google.com/…. Ref. therein might be what you are looking for, but it's been published in Moscow, likely in Russian. $\endgroup$
    – udrv
    Commented Aug 3, 2016 at 4:48

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The phase change of a charge particle moving in a magnetic field is usually obtained by a gauge argument. See section 5.4 of this paper which discusses the Aharanov-Bohm effect. Using simple arguments you can deduce the perimeter law for the phase, e.g., the phase picked up is $i(2\pi r)A$ (see the equation on page 49). I work in condensed matter physics so I do not know the corresponding argument for the strong force, but I imagine it is similarly a geometric picture and can be deduced from an appropriate gauge transformation.

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