Phase anholonomy in the classical adiabatic motion of charged particles

The classical adiabatic motion of charged particles in strong magnetic fields, otherwise known as guiding center motion, exhibits an anholonomic phase similar to Berry's phase and the phase discovered in a general context by Hannay. Analysis of this effect reveals that there often is no best way to define the gyrophase when magnetic field lines are curved. Instead, a change in the definition of the phase is a kind of gauge transformation, the study of which leads to new insight into guiding center theory. The path-dependent phase that occurs in this problem is coupled with the metrical structure of physical space, giving rise to a transport process for vectors and frames which is similar to parallel transport in non-Euclidean geometry. Strong analogies with Fermi-Walker transport and Thomas precession in special relativity are pointed out