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Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames

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arxiv 2003.04304 v5 pith:ZZ3ZP5FJ submitted 2020-03-06 gr-qc astro-ph.COhep-th

Gabriele Gionti , S.J This is my paper · ORCID
classification gr-qcastro-ph.COhep-th
keywords hamiltonianjordantheorybrans-dickecanonicaleinsteinframetransformation
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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.

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Cited by 1 Pith paper

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  1. Canonical Clock Sectors and Relational Frame Equivalence in Brans--Dicke Theory

    gr-qc 2026-07 accept novelty 6.0 of 10

    Apparent Jordan–Einstein inequivalence after relational deparametrization is a clock-sector mismatch; a frame-adapted canonical chart restores identical reduced Hamiltonians.

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