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 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.