  We demonstrate for the first time and unexpectedly that the Principle of
Relativity dictates the choice of the "gauge conditions" in the canonical
example of a Gauge Theory namely Classical Electromagnetism. All the known
"gauge conditions" of the literature are interpreted physically as
electromagnetic continuity equations hence the "gauge fields". The existence of
a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is
the crux of the problem [1]. A phase-space with the domains of validity of the
various "gauge conditions" is provided and is shown to depend on three
characteristic times : the magnetic diffusion time, the charge relaxation time
and the transit time of electromagnetic waves in a continuous medium [2].
