Berry phase without a magnetic field

It is common to calculate Berry phases for quantum systems in, for example, a magnetic field. In this case we compute the Berry phase ##\gamma## using

$$\gamma[C] = i\oint_C \! \langle n,t| \left( \vec{\nabla}_R |n,t\rangle \right)\,\cdot{d\vec{R}} \,$$

where ##R## parametrizes the cyclic adiabatic process, in this case, the magnetic field.

I was wondering what the Berry phase is for a system that has no external fields. Say, you have a particle in a box and the box rotates in three-dimensional box about some point. How do you compute the Berry phase for this system?

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PeterDonis
Mentor
2019 Award
Taken at face value, your equation says that the Berry phase is zero if the magnetic field is zero. Do you have some reason to think that should not be the case?