So ##k\cdot k'=\sum_{over all \alpha} k_\alpha k'^\alpha## right?
Within the same book when they mention the 4-vector, they wrote p (without the above arrow). Normal vector they wrote ##\vec p## or ##\bf p## and ##p^\mu## is the contravariant vector, which is ##p^\mu=(E, p_x, p_y, p_z)##
Then I...