Relativistic momentum ($\mathbf{p}=\gamma m\mathbf{v}$)

For a massive particle, its spatial momentum in an inertial frame is $\gamma m\mathbf{v}$, with m its invariant rest mass and $\gamma$ the Lorentz factor. Together with its relativistic energy it forms the four-momentum. In a magnetic quadrupole's paraxial approximation, replacing $mv$ by the longitudinal momentum extends the transverse focusing scale to relativistic beams.