Gradient Four-Vector

The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is

 del _mu=[1/cpartial/(partialt); partial/(partialx); partial/(partialy); partial/(partialz)],

which can be written

 (del ^mu)^2= square ^2,

where  square ^2 is the d'Alembertian.

See also

d'Alembertian, Gradient, Tensor, Vector

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Morse, P. M. and Feshbach, H. "The Differential Operator del ." §1.4 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 31-44, 1953.

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Gradient Four-Vector

Cite this as:

Weisstein, Eric W. "Gradient Four-Vector." From MathWorld--A Wolfram Web Resource.

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