Twisted Classical Phase Spaces: A Consequence of the Quantum Indistinguishability of Interacting Spins

We argue that in systems with finite Hilbert spaces, the quantum-kinematical constraint imposed by the identity of particles on the associated Hilbert spaces has a classical counterpart: the corresponding classical phase spaces exhibit non-trivial topological differences depending on whether such particles are distinguishable or not. We show this explicitly in the context of the two-interacting-spin model with axial anisotropy.