Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory

Abstract

We carefully perform a Hamiltonian Dirac's constraint analysis of $\omega =-\frac{3}{2}$ Brans-Dicke theory with Gibbons-Hawking-York (GHY) boundary term. The Poisson brackets are computed via functional derivatives. After a brief summary of the results for $\omega \ne -\frac{3}{2}$ case, we derive all Hamiltonian Dirac's constraints and constraint algebra both in the Jordan and Einstein frames. Confronting and contrasting Dirac's constraint algebra in both frames, it is shown that they are not equivalent. This highlights the transformations from the Jordan to the Einstein frames are not Hamiltonian canonical transformations.

corrected some typos, more references added

References in corpus (5)

• The (pseudo)issue of the conformal frame revisited
• Physical non-equivalence of the Jordan and Einstein frames
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Note on stability in conformally connected frames

Cited by in corpus (4)

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• Casimir Wormholes in Brans-Dicke Theory
• Again About Singularity Crossing In Gravitation And Cosmology