Possibility of dynamical symmetry restoration in the Gaussian overlap approximation

We analyze the symmetry-conserving-variational-dynamics and the time-dependent-generator-coordinate methods showing their equivalence for a large class of problems. The application to actual calculations involving the restoration of the rotational symmetry in nuclear dynamics is examined together with the Gaussian overlap hypothesis. It is shown that the range of validity of the combined approach is restricted to very weak symmetry breaking. The relative location of the method in the context of variational approximations to the dynamics is established as well as the various relations among different procedures