Projected Linear Response Theory for Charge-Exchange Excitations and Double Beta Decay

The projected random phase approximation (PRPA) for charge-exchange excitations is derived from the time-dependent variational principle. Explicit results for the unperturbed energies (including the self-energy corrections), the PRPA matrices, and the transition matrix elements are presented. The effect of the projection procedure on the two-neutrino $\beta\beta$ decay in $^{76}Ge$ is briefly discussed.