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 succintly expressed in this notation:

In order to expresse partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variales with indices such as $x_{0}$, $x_{1}$, $x_{2}$, $∂_{0}$, $∂_{1}$ and $∂_{2}$ instead of the usual letters $x$, $y$ and $z$.