  The formalism of quantum mechanics is presented in a way that its
interpretation as a classical field theory is emphasized. Two coupled real
fields are defined with given equations of motion. Densities and currents
associated to the fields are found with their corresponding conserved
quantities. The behavior of these quantities under a galilean transformation
suggest the association of the fields with a quantum mechanical free particle.
An external potential is introduced in the Lagrange formalism. The description
is equivalent to the conventional Schr\"odinger equation treatment of a
particle. We discuss the attempts to build an interpretation of quantum
mechanics based on this scheme. The fields become the primary onthology of the
theory and the particles appear as emergent properties of the fields. These
interpretations face serious problems for systems with many degrees of freedom.
