  It has been widely thought that the wave function describes a real, physical
field in a realist interpretation of quantum mechanics. In this paper, I
present a new analysis of the field ontology for the wave function. First, I
argue that the non-existence of self-interactions for a quantum system such as
an electron poses a puzzle for the field ontologists. If the wave function
represents a physical field, then it seems odd that there are (electromagnetic
and gravitational) interactions between the fields of two electrons but no
interactions between two parts of the field of an electron. Next, I argue that
the three solutions a field ontologist may provide are not fully satisfactory.
Finally, I propose a solution of this puzzle that leads to a particle
ontological interpretation of the wave function.
