4-current

This MedLibrary.org supplementary page on 4-current is provided directly from the open source Wikipedia as a service to our readers. Please see the note below on authorship of this content, as well as the Wikipedia usage guidelines. To search for other content from our encyclopedia supplement, please use the form below:

Related Sponsors

BM Pharmacy Generic pharmaceuticals at unbeatable prices. Insomnia, men's health, hair health, pain control. bmpharmacy.com
Online Pharmacy Carisoprodol, tadalafil, sildenafil, vardenafil and more... xlpharmacy.com
MedBasket.com Discreet. Inexpensive. Fast shipping. Great selection. What more can we say? medbasket.com
Frugalmed 2000 reasons to shop with us first. frugalmed.com
Ads by Tiva

 This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. (September 2008)

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. Its four components are given by:

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_i J^i

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.

See also

Wikipedia content modification information:

  • This page was last modified on 26 December 2008, at 14:52.

Wikipedia Authorship and Review

Wikipedia content provided here is not reviewed directly by MedLibrary.org. Wikipedia content is authored by an open community of volunteers and is not produced by or in any way affiliated with MedLibrary.org.

Wikipedia Usage Guidelines

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article on "4-current".

The URL for this specific entry is:

All Wikipedia text is available under the terms of the GNU Free Documentation License. (See Copyrights for details). Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc.