A brief note on Weyl frames and canonical transformations in geometrical scalar–tensor theories of gravity

We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that for time-lapse extended Robertson-Walker metrics in the ADM formalism a class of Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.