The archetypical gauge theory is the Heaviside – Gibbs formulation of continuum electrodynamics in terms of an electromagnetic four-potential, which is presented here in space/time asymmetric Heaviside notation. The electric field E and magnetic field B of Maxwell's equations contain only "physical" degrees of freedom, in the sense that every mathematical degree of freedom in an electromagnetic field configuration has a separately measurable effect on the motions of test charges in the vicinity. These "field strength" variables can be expressed in terms of the electric scalar potential φ φ and the magnetic vector potential A through the relations: E = − − ∇ ∇ φ φ − − ∂ ∂ A ∂ ∂ t , B = ∇ ∇ × × A .