Jordan and Einstein Frames from the perspective of $\omega=3/2$ Hamiltonian BransDicke theory
Abstract
We carefully perform a Hamiltonian Dirac's constraint analysis of $\omega=\frac{3}{2}$ BransDicke theory with GibbonsHawkingYork (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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.12222
 Bibcode:
 2021arXiv211012222G
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 corrected some typos, more references added