d'Alembertian - Aetherwisp

The d'Alembertian or d'Alembert operator $\square ^{2}$ is a differential operator that can be seen as an extension to the Laplacian operator. It is defined as

\square ^{2}\equiv \nabla ^{2}- \frac{1}{v^{2}}\frac{ \partial ^{2} }{ \partial t^{2} }

where $v\in \mathbb{R}$ . It appears commonly in the physics, where $t$ is interpreted as time, and specifically in wave phenomena, where it defines the wave equation $\square ^{2}\psi=0$ and $v$ is interpreted as wave propagation speed. In the context of special relativity, the d'Alembertian readily works as a spacetime Laplacian and is alternatively defined as

\square ^{2}\equiv \frac{ \partial }{ \partial x_{\nu} } \frac{ \partial }{ \partial x^{\nu} }