Write down the position four-vector. Suppose this represents the position of a particle with rest mass $M$ and velocity v. Show that the four momentum of the particle is

$$p_{a}=(M \gamma c, M \gamma \mathbf{v})$$

where $\gamma=\left(1-|\mathbf{v}|^{2} / c^{2}\right)^{-1 / 2}$.

For a particle of zero rest mass show that

$$p_{a}=(|\mathbf{p}|, \mathbf{p})$$

where $\mathbf{p}$ is the three momentum.