Jordan and Einstein frames from the perspective of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math> Hamiltonian Brans-Dicke theory

We carefully perform a Hamiltonian Dirac's constraint analysis of the $\ensuremath{\omega}=\ensuremath{-}\frac{3}{2}$ Brans-Dicke theory with Gibbons-Hawking-York boundary term. The Poisson brackets are computed via functional derivatives. After brief summary results for $\ensuremath{\omega}\ensuremath{\ne}\ensuremath{-}\frac{3}{2}$ case [G. Gionti S. J., Canonical addresses inequivalence between Jordan and Einstein frames, Phys. Rev. D 103, 024022 (2021)] we derive all constraints algebra in both frames. Confronting contrasting it is shown that they not equivalent. This highlights transformations from to frames canonical transformations.