D'Alembert operator

From Academic Kids

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

<math>\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}.<math>

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.

Template:Maths-stubde:D'Alembertoperator

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