We intend to clarify the interplay between boundary terms and conformal
transformations in scalar-tensor theories of gravity. We first consider the
action for pure gravity in five dimensions and show that, on compactifing a la
Kaluza-Klein to four dimensions, one obtains the correct boundary terms in the
Jordan (or String) Frame form of the Brans-Dicke action. Further, we analyze
how the boundary terms change under the conformal transformations which lead to
the Pauli (or Einstein) frame and to the non-minimally coupled massless scalar
field. In particular, we study the behaviour of the total energy in
asymptotically flat space-times as it results from surface terms in the
Hamiltonian formalism.Comment: LaTeX 2e, 12 pages, no figure
