  We propose the generally covariant action for the theory of a self-coupled
complex scalar field and electromagnetism which by virtue of constraints is
equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics
(MHD). We recover from it the Euler equation with Lorentz force, and the
thermodynamic relations for a prefect fluid. The equation of state of the
latter is related to the scalar field's self potential. We introduce 1+3
notation to elucidate the relation between MHD and field variables. In our
approach the requirement that the scalar field be single valued leads to the
quantization of a certain circulation in steps of $\hbar$; this feature leads,
in the classical limit, to the conservation of that circulation. The
circulation is identical to that in Oron's generalization of Kelvin's
circulation theorem to perfect MHD; we here characterize the new conserved
helicity associated with it. We also demonstrate the existence for MHD of two
Bernoulli-like theorems for each spacetime symmetry of the flow and geometry;
one of these is pertinent to suitably defined potential flow. We exhibit the
conserved quantities explicitly in the case that two symmetries are
simultaneously present, and give examples. Also in this case we exhibit a new
conserved MHD circulation distinct from Oron's, and provide an example.
