In Section 2.2 we will work in a gauge where the TDVP is identically zero, which is a possible choice of gauge only for one-dimensional problems (in nuclear space), as those presented in Section 3. Another possible choice of gauge in high-dimensional situations, is to put to zero the TDVP along a "selected" direction in nuclear configuration space. Then, one could combine a classical and a quantum trajectory-based representation of nuclear dynamics, adopting the refined quantum description only along the "selected" direction.