Four-current

J^a = \left(c 
ho, \mathbf{j} 
ight)

where

c

:ρ the Charge Density
:j the conventional Current Density .

In SI , the current density is defined as

:

J^a = \left(rac
ho{\epsilon_0}, \mu_0\mathbf j
ight)

where

ε

μ

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 = rac{\partial 
ho}{\partial t} + 
abla \cdot \mathbf{j} = 0

where ''D'' is an operator called the Four-gradient and given by (1/c ∂/∂t, -∇). 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 Noether's Theorem .

	CATEGORIES ABOUT FOUR-CURRENT

	electromagnetism

	minkowski spacetime

	relativity

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