  Jordan and Einstein frame are studied under the light of Hamiltonian
formalism. Dirac's constraint theory for Hamiltonian systems is applied to
Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame,
Brans-Dicke theory has four secondary first class constraints and their
constraint algebra is closed. We show, contrary to what is generally believed,
the Weyl (conformal) transformation, between the two frames, is not a canonical
transformation, in the sense of Hamiltonian formalism. This addresses quantum
mechanical inequivalence as well. A canonical transformation is shown.
