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Four-gradient - Wikipedia, the free encyclopedia

Four-gradient

From Wikipedia, the free encyclopedia

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The four-gradient is the four-vector generalization of the gradient:

$\partial_\alpha \ \stackrel{\mathrm{def}}{=}\ \left(\frac{1}{c} \frac{\partial}{\partial t}, \nabla \right)$

and is sometimes also represented as D.

The square of D is the four-Laplacian, which is called the d'Alembert operator:

$D\cdot D = \partial_\alpha \partial^\alpha = - \frac{1}{c^2}\frac{\partial^2}{\partial t^2} + \nabla^2$ .

As it is the dot product of two four-vectors, the d'Alembertian is a Lorentz invariant scalar.

It is also written $\Box$

This geometry-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "http://en.wikipedia.org../../../f/o/u/Four-gradient.html"

Categories: Geometry stubs | Relativity

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