Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

The permutation symmetry of quantum mechanics is widely thought to imply a sort of metaphysical underdetermination about the identity of particles. Despite claims to the contrary, this implication does not hold in the more fundamental quantum field theory, where an ontology of particles is not generally available. Although permutations are often defined as acting on particles, a more general account of permutation symmetry can be formulated using superselection theory. As a result, permutation symmetry applies even in field theories with no particle interpretation. The quantum mechanical account of permutations acting on particles is recovered as a special case.