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# General Relativity and Quantum Cosmology

# Title: Jordan and Einstein Frames from the perspective of $ω=-3/2$ Hamiltonian Brans-Dicke theory

(Submitted on 23 Oct 2021 (v1), last revised 11 Nov 2021 (this version, v2))

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 $\omega\neq-\frac{3}{2}$ 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.

## Submission history

From: Gabriele Gionti S.J. [view email]**[v1]**Sat, 23 Oct 2021 13:58:47 GMT (79kb)

**[v2]**Thu, 11 Nov 2021 19:45:14 GMT (80kb)

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