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I have been using results from this paper in calculations. In sections 2.4 and 3.4 they perform a canonical transformation into new coordinates consisting of constants of motion.

My question is specifically about eq. 2.65. There they claim that the flow generated by $H_0$ on some observable $f$ is given by the Poisson bracket $\{H_0, f\}$. To me this seems entirely backwards as for example Hamiltonian flows are given by the bracket $\{\cdot, H\}$.

However it's entirely possible that my Hamiltonian mechanics is simply too rusty.

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    $\begingroup$ It is a historically non-standard sign convention, but I like use the same convention as these authors as it minimizes the number of minus signs in other places. I always stress that I am using a non standard convention in published papares though. $\endgroup$
    – mike stone
    Commented Apr 11 at 0:03
  • $\begingroup$ The problem is that they seem to mix up different conventions as in (2.56) they write the Hamiltonian equations and sue the opposite convention to (2.65) $\endgroup$
    – Geigercounter
    Commented Apr 11 at 8:00

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