field theory. This is mostly harmless, since if either one particle type is stationary or the relative motion is collinear, then the right result is obtained from the incorrect formulas. The formula is invariant, but not manifestly so. It can be rewritten in terms of four-velocities as The correct expression for the flux, published by Christian Møller in 1945, is given by One notes that for collinear velocities, . In order to get a manifestly Lorentz invariant expression one writes with , where is the density in the rest frame, for the individual particle fluxes and arrives at In the literature the quantity as well as are both referred to as the relative velocity. In some cases (statistical physics and dark matter literature), is referred to as the Møller velocity'', in which case means relative velocity. The true relative velocity is at any rate . The discrepancy between and is relevant though in most cases velocities are collinear. At LHC the crossing angle is small, around 300 rad, but at the old Intersecting Storage Ring at CERN, it was about 18◦. See also Hyperbolic law of cosines Biquaternion Remarks Notes References (graduate level) (introductory level) (graduate level) Historical Wikisource version External links Special relativity Equations Velocity Kinematics