Assume that $k$ and $p$ are four-vectors. How do I get the explicit form of $k^\mu p^\mu$? And is it the same value as $k \cdot p \cdot I_{4×4} $?
I am confused because the index is repeated but is not contracted.
If it makes any difference, assume that the metric tensor is a diagonal tensor $(1, -1, -1, -1)$.
Never mind I thought about it. The resultant vector will be
$$(k^0 p^0, k^1 p^1, k^2 p^2, k^3 p^3) = (k^0 p^0, \vec{k} \cdot \vec{p}) $$
Which is, in fact, not the same as $k⋅p⋅I4×4$.