This article has left me confused. I don't see how this notion of phase relates back to a locally-evolving amplitude distribution over a space of configurations, if those configurations are merely the locations of some indistinguishable lumps in a field. How do these phases become manifest in the configuration space? It seems like there must be more to the configuration space than just a set of locations for each type of "particle", but previous articles have claimed otherwise.

The configuration space is a field where there's a number at each place. This
number is a complex number.
Does that help?

0Klao12y

This left me totally confused too.
But then, I realized that there is a property of photons that can help with this
confusion here: spin. So, the configuration space is not a "a photon here and a
photon there...", but a "a photon with a +1 spin here, a photon with -1 spin
there..." And then this phase thing arises from the values of the amplitude
distribution for the configurations with photons of opposite spins. This makes
the math quite a bit easier too.
I might be completely mistaken about this, though.

This article has left me confused. I don't see how this notion of phase relates back to a locally-evolving amplitude distribution over a space of configurations, if those configurations are merely the locations of some indistinguishable lumps in a field. How do these phases become manifest in the configuration space? It seems like there must be more to the configuration space than just a set of locations for each type of "particle", but previous articles have claimed otherwise.