In condensed matter physics: If we describe e.g. an exciton as a combination of an electron and a hole, do we need to combine them in a Slater determinant or into a simple product state? What happens with exchange interactions?
A hole is an abstraction of a missing electron, that is of a many electron system with spin 1/2. The wave function of the total system is antisymmetric under exchange of participating electrons. This implies that there us an exchange interaction between the electron and the hole.