4-momentum

Including a time element of energy as

$𝐩=(\frac{E}{c},p^x,p^y,p^z)$

This four element vector transforms as a tensor

$p{\text{'}}^{\mu }=\frac{\partial x{\text{'}}^{\mu }}{\partial x^{\nu }}{p}^{\nu }$

And as such constitutes a four-vector, a rank 1 tensor, called the 4-momentum. The mass of a particle is an invariant given by the spacetime length of the 4-momentum according to

$m^2{c}^2=g_{\mu \nu }{p}^{\mu }{p}^{\nu }$

which for the metric of special relativity yeilds

$E^2=p^2{c}^2+m^2{c}^4$

For a particle with mass, the 4-momentum can be related to the 4-velocity by

$p^{\mu }=m{U}^{\mu }$