Rapidity ($\theta =\mathrm{artanh}v$)

For one spatial dimension and $c=1$, a massive particle has $v=\tanh \theta$, $E=M\cosh \theta$ and $p=M\sinh \theta$. A Lorentz boost adds a constant to all rapidities, so a rapidity difference is invariant. Rapidity is useful for factorized scattering, where two-body S-matrices depend only on that difference.