Extending exchange symmetry beyond bosons and fermions

We study quantum many-body states of particles subject to a more general exchange symmetry than the behavior under pairwise exchange obeyed by bosons and fermions. We refer to these hypothetical particles as immanons because the scalar product of states with the generalized exchange symmetry is the immanant of the matrix containing all mutual scalar products of the occupied single-particle states, a generalization of the determinant and permanent applied for fermions and bosons. Immanons are shown to obey a partial Pauli principle that forbids the occupation of single-particle states above certain threshold numbers. This has measurable consequences for their tendency to favor or oppose multiple occupation of single-particle modes, and it links conjectured mathematical properties of immanants to the expected outcome of a physical Gedanken experiment.