Probability distribution for the relative velocity of colliding particles in a relativistic classical gas

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Notations: we use natural units with ℏ = c = k B = 1 \hbar=c=k_{B}=1 and Lorentz metric g = ( 1 , − 1 , − 1 , − 1 ) g=(1,-1,-1,-1) . We use ’probability distribution’ for normalized probability density function (p.d.f.), ∫ d x f ( x ) = 1 \int dxf(x)=1
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