# ultrarelativistic gas

Consider the ideal ultrarelativistic gas Hamiltonian $\mathbf{H = }\sum_{i = 1}^N \mathbf{c |\vec{p_{i}}|}$, now if we let molecules to interact with a potential term like $\mathbf{d|\vec{q_{i}}|}$; is it still possible to find density of states $\omega(E)$?

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What is this 'ultra-relativistic gas Hamiltonian', have you got a reference for this? –  Killercam Feb 16 '13 at 15:02
@Killercam $E^2=m^2c^4+p^2c^2$. Ultrarelativistic means $cp >> mc^2$ so that $E\approx cp$ –  Jorge Feb 17 '13 at 19:18
Thanks for that, but that was not my question... –  Killercam Feb 17 '13 at 19:24
If the system is at equilibrium then $w$ is proportional to $\exp(-\beta H)$. This result is independent of the specific form of $H$.