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I Hamiltonian as the generator of time translations

  1. Sep 9, 2016 #1
    In literature I have read it is said that the Hamiltonian ##H## is the generator of time translations. Why is this the case? Where does this statement derive from?

    Does it follow from the observation that, for a given function ##F(q,p)##, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial F}{\partial t}$$ In particular, if ##F## is not explicitly dependent on time, then $$\frac{dF}{dt}=\lbrace F,H\rbrace $$ Or is there more to it?
  2. jcsd
  3. Sep 10, 2016 #2
    Ah poisson brackets!

    I think what you are looking for is Noethers theorem.

    Susskinds classical mechanics course on youtube, i think lecture 4 (symmetries) and 8 (poisson) will help you.
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