Symmetrization and Fock Space

The assertion that quantum states of same-type particles have to be symmetrized because they are indistinguishable has led to a debate in the foundations of quantum mechanics around topics like “thisness” of particles and “surplus structure” in spaces of quantum states. We analyze the underlying mathematical notions and find that a central issue lies in the a priori identification of n-particle Fock space with the n-fold tensor product of single-particle spaces and the corresponding failure to recognize that multi-particle quantum states are ultimately the result of actions of Hamiltonians.