Electromagnetic Four-potential

The electromagnetic four-potential can be defined as:

SI units	cgs units

in which ϕ is the electric potential, and A is the magnetic potential (a vector potential). The units of Aα are V·s·m−1 in SI, and Mx·cm−1 in Gaussian-cgs.

The electric and magnetic fields associated with these four-potentials are:

SI units	cgs units

In special relativity, the electric and magnetic fields must be written in the form of a tensor so they transform correctly under Lorentz transformations - the electromagnetic tensor). This is written in terms of the electromagnetic four-potential as:

This essentially defines the four-potential in terms of physically observable quantities.