Metastable states,the adiabatic theorem and parity violating geometric phases I

A system of metastable plus unstable states is discussed. The mass matrix governing the time development of the system is supposed to vary slowly with time. The adiabatic limit for this case is studied and it is shown that only the metastable states obtain the analogs of the dynamical and geometrical phase factors familiar from stable states. Abelian and non-Abelian geometric phase factors for metastable states are defined.