Time-dependent gauge transformations and Berry's phase

Abstract

The time-dependent gauge transformation is discussed in the context of modified Lagrangian and Hamiltonian formalisms in which time is treated as a dynamical coordinate. It is shown that Berry's phase is invariant under both time-dependent unitary and generalized gauge transformations. The Berry phase is therefore unique. It is then demonstrated that the Berry phase can be shifted into the dynamical part of the total phase by choosing a new set of instantaneous eigenstates which are associated with a different gauge. This procedure breaks the gauge equivalence and also changes the dynamics of the system considered.