Einstein notation for partial derivatives

The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.

In particular, the divergence and the Laplacian can be succinctly expressed in this notation:

In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as $x_0$, $x_1$, $x_2$, ${\partial }_0$, ${\partial }_1$ and ${\partial }_2$ instead of the usual letters $x$, $y$ and $z$.