Canonical analysis of Brans-Dicke theory addresses Hamiltonian inequivalence between the Jordan and Einstein frames

YThe Jordan and Einstein frames are studied under the light of the Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan frame. In both the Jordan and Einstein frames, 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 the Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.

Automated summary

This study explores the Jordan and Einstein frames in the context of Hamiltonian formalism, analyzing the Brans-Dicke theory using Dirac's constraint theory. Contrary to popular belief, the Weyl transformation between these frames is not considered a canonical transformation in the Hamiltonian formalism, highlighting quantum mechanical inequivalence. Additionally, a canonical transformation is demonstrated in the study.