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A Lorentz invariant phase space - symplectic geometry

  1. Nov 5, 2018 #1
    I have an assignment to show that specific intensity over frequency cubed [tex]\frac{I}{\nu^3},[/tex] is Lorentz invariant and one of the main topics there is to show that the phase space is Lorentz invariant. I did it by following J. Goodman paper, but my professor wants me to show this in another way, using symplectic geometry (wedge products), which I am not really familiar with and Liouville's theorem. I found this on Wiki stating that "that the Lie derivative of volume form is zero along every Hamiltonian vector field." Does this prove the also Lorentz invariance?

    Also I found these notes on symplectic geometry (chapter 13 on p76). Does the statement that [itex]\omega[/itex] is closed (or [itex]d\omega = 0[/itex]), mean that it is invariant? Is this proof enough for Lorentz invariance?
     
    Last edited: Nov 5, 2018
  2. jcsd
  3. Nov 10, 2018 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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