The AC/DC Interfaces > Theory of Magnetic Fields > Gauge Transformations

Gauge Transformations
The electric and magnetic potentials are not uniquely defined from the electric and magnetic fields through
Introducing two new potentials
gives the same electric and magnetic fields:
The variable transformation of the potentials is called a gauge transformation. To obtain a unique solution, choose the gauge—that is, put constraints on Ψ that make the solution unique. Another way of expressing this additional condition is to put a constraint on  · A. A vector field is uniquely defined up to a constant if both  · A and ∇ × A are given. This is called Helmholtz’s theorem.
One particular gauge is the Coulomb gauge given by the constraint: ∇ ⋅ A = 0.