Quantum permutations are not qualitative isomorphisms (and what this tells us about haecceitism)

Permutations play an important role in both metaphysics and philosophy of physics: metaphysicians are interested in how (if at all) possible worlds are affected by permutations of the objects that inhabit those worlds; philosophers of physics are interested in how (if at all) permutations affect physical states of quantum systems. In the literature on the metaphysical implications of permutation invariance in quantum mechanics, it is standard to identify the two. In this paper, I argue that this identification is mistaken and investigate the metaphysical consequences of this conclusion.