The abstract already lost me: "Thus the Schroedinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for a

The abstract already lost me: "Thus the Schroedinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point." But the wave function lives on the configuration space of the system: if you have $N$ particles, the wave function lives on $R^{3N}$. In what way is this a "space-filling physical field"? Admittedly I haven't had time to do more than skim the article; perhaps it's explained more carefully later on. (Off-topic, but since this has come up a number of times on HN: this point is also where Bohmian pilot wave theory has never been wholly satisfying for me. If you accept the pilot wave picture, then the double slit loses a little bit of its mystery, but many-body theory still seems just as weird as before.)