D'Alembert Operator - Alternate Notations

Alternate Notations

There are a variety of notations for the d'Alembertian. The most common is the symbol : the four sides of the box representing the four dimensions of space-time and the which emphasizes the scalar property through the squared term (much like the Laplacian). This symbol is sometimes called the quabla (cf. nabla symbol). In keeping with the triangular notation for the Laplacian sometimes is used.

Another way to write the d'Alembertian in flat standard coordinates is . This notation is used extensively in quantum field theory where partial derivatives are usually indexed: so the lack of an index with the squared partial derivative signals the presence of the D'Alembertian.

Sometimes is used to represent the four-dimensional Levi-Civita covariant derivative. The symbol is then used to represent the space derivatives, but this is coordinate chart dependent.