Yeah, I found that weird too, but apparently the paper says that this is mathematically equivalent if they also use virtual phonons, which is interesting indeed

Yeah, I found that weird too, but apparently the paper says that this is mathematically equivalent if they also use virtual phonons, which is interesting indeed. I wonder if these are collective excitations (the boson equivalent of quasiparticles) instead of something similar to Cooper pairing. I haven't read the paper though, so this is just me thinking out loud.