The Ontological Status of Wave Function

Mathematical entities, in physics, are used to represent the ontology of theories. But there is a distinction between mathematical entities and physical entities which mathematics refers to, and ignoring this distinction leads to strange and false conclusions. This paper aims to realize, in a realistic interpretation, what the wavefunction, as a mathematical entity, refers to.. It is emphasized that the confusion of the wave function as a mathematical element with the physical state leads to a strange conclusion that the dimensions of the physical space are in direct correspondence with the mathematical dimensions, or the configuration space is a real physical space. Moreover,It is suggested, that determination of the ontological status of the wave function needs a theory to connect and explain the relation between local beables and quantum state.