Added to Favorites

Related Searches

Definitions

In special and general relativity, the four-current is the Lorentz covariant four-vector that replaces the electromagnetic current density, or indeed any conventional charge current density.## See also

- $J^a\; =\; left(c\; rho,\; mathbf\{j\}\; right)$

where

- c is the speed of light

- ρ the charge density

- j the conventional current density.

- a labels the space-time dimensions

In special relativity, the statement of charge conservation (also called the continuity equation) is that the Lorentz invariant divergence of J is zero:

- $D\; cdot\; J\; =\; partial\_a\; J^a\; =\; frac\{partial\; rho\}\{partial\; t\}\; +\; nabla\; cdot\; mathbf\{j\}\; =\; 0$

where D is an operator called the four-gradient and given by (1/c ∂/∂t, ∇). The summation convention has been used, so that the space-time dimensions are implicitly summed over. i.e.

- $partial\_a\; J^a\; =\; sum\_\{i=0\}^\{3\}\; partial\_a\; J^a$

Sometimes, the above relation is written as

$J^a\{\}\_\{,a\}=0,$

In general relativity, the continuity equation is written as:

$J^a\{\}\_\{;a\}=0,$

where the semi-colon represents a covariant derivative.

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)

This article is licensed under the GNU Free Documentation License.

Last updated on Thursday September 25, 2008 at 13:34:50 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

This article is licensed under the GNU Free Documentation License.

Last updated on Thursday September 25, 2008 at 13:34:50 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

Copyright © 2015 Dictionary.com, LLC. All rights reserved.