The Berry phase for a threefold degenerate state

Abstract
Different expressions for calculating the Berry phase of adiabatic processes are reviewed and their limitations are discussed. These expressions are then applied to the case of a circuit surrounding a triple degeneracy. It is shown that the most general formula for the Berry phase requires the use of the full SU(3) invariance group of a T state coupled to in + tau 1+ tau 2 modes. The T*( in + tau 2) Jahn-Teller problem appears as a special case with SO(3) symmetry.