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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# A Lorentz invariant phase space - symplectic geometry

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