Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than separating time from three-dimensional space.
Charges (free or as a distribution) at rest will appear to remain at the same spatial position for some interval of time (as long as they're stationary).
In general relativity, the continuity equation is written as: where the semi-colon represents a covariant derivative.
The four-current appears in two equivalent formulations of Maxwell's equations, in terms of the four-potential[5] when the Lorenz gauge condition is fulfilled: where
is the D'Alembert operator, or the electromagnetic field tensor: where μ0 is the permeability of free space and ∇α is the covariant derivative.
[6] In 1956 Semyon Gershtein and Yakov Zeldovich considered the conserved vector current (CVC) hypothesis for electroweak interactions.