  Lorentz invariant scalar functions of the magnetic field are defined in an
ideal relativistic plasma. These invariants are advected by the plasma fluid
motion and play the role of the {\it potential magnetic field} introduced by R.
Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these
invariants we recover the Cauchy conditions for the magnetic field components
in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure
allows us to formulate Alfv\`en theorem for the conservation of the magnetic
flux through a surface comoving with the plasma in a Lorentz invariant form.
