info prev up next book cdrom email home

Gradient Four-Vector

The 4-dimensional version of the Gradient, encountered frequently in general relativity and special relativity, is

\nabla_\mu =\left[{\matrix{
{1\over c} {\partial\over\partia...
...tial\over\partial y}\cr
{\partial\over\partial z}\cr}}\right],

which can be written

(\nabla^\mu)^2\equiv \vbox{\hrule height.6pt\hbox{\vrule wid...
...t height6pt \kern6.4pt \vrule width.6pt}
\hrule height.6pt}^2,

where $\vbox{\hrule height.6pt\hbox{\vrule width.6pt height6pt \kern6.4pt \vrule width.6pt}
\hrule height.6pt}^2$ is the d'Alembertian Operator.

See also d'Alembertian Operator, Gradient, Tensor, Vector


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

© 1996-9 Eric W. Weisstein