The Ultimate D'Alembertian operator - American History Information Guide and Reference

In special relativity and electromagnetism and wave theory, the d'Alembertian operator is the Laplace operator of Minkowski space. Thus in the standard coordinate basis, where $| g | = 1$ , it has the form

$\Box := \Delta_{\mathbf{M}} = \partial_i \partial^i = -\partial_0^2 + \sum_{i=1}^3 \partial_i^2 = \Delta_{\mathbf{R}^3} - \frac{\partial^2}{c^2\partial t^2}.$

Clearly the sign of these expressions depend on the sign convention used for the Minkowski metric.

Lorentz transformations leave the metric invariant, thus the above coordinate expressions remain valid in every inertial frame.

Categories: Multivariate calculus

Last updated: 05-10-2005 01:49:26

Your American History Reference Guide! - D'Alembertian operator

D'Alembertian operator

Your American History Reference Guide!
- D'Alembertian operator